@washboat Buddy, I hate to inform you that almost all of your mathematics educators are idiots who have never understood the concept of number, never mind mathematics. I am a real mathematician and educator. studio.ua-cam.com/channels/lBbBVLs3M-d3dNgU4Vop_A.html
This is beautiful. It *is* just the same machinations as the quadratic formula, but as an algorithm, its steps are much more intuitive. You are simply turning an arbitrary parabola into a "unit parabola" 1) set r.h.s. To 0 (set the y component to 0) 2) divide by "a" (scale the parabola to coefficient of 1) 3) find b/2 (average of x component of both roots, center parabola on the x-axis) 4) solve for "u" (hard to put in words, but this "coordinates" the focus with the roots) It's all just translation and scaling, which is much easier to "get" for us (3+t)-dimensional beings than abstract algebra, especially at a young age. I'd love to see 3blue1brown animate why this works.
I adore how excited and enthusiastic he is. I hated the process of guessing and checking as a kid stressed out on a test. His method is gorgeous and I can appreciate why it's exciting.
This as a pedagogy for 15 yr olds will be much better for me. It also triggered me to think about how to present when you have an "a" term, and a much cleaner method of deriving the formula. Most kids just blank stare when I derive via completing the squares and I just end up saying "remember the formula". Thanks mate!
I was inspired to come up with this precisely because I have received the blank stare from students when I derive the quadratic formula in the usual way. It is nice to hear from a fellow educator. The perspective from the front lines of teaching school age students is something that can only be developed by actually doing it.
"Completing the square" is where you loose your class. People are following along and everything is going well and then you say "imagine some random numbers that make this work" and people think its witchcraft.
Thank you so much! I'd been struggling with solving quadratic equations because I'd just be *stuck* trying to factor 2 numbers that add and multiply to two different numbers. This is a comprehensive and easy to understand strategy that I will use from now on!
Seems familiar now also. It is possible to work up a fairly straight forward working spreadsheet that gives valid results for even cases where the results include imaginary numbers in the results. That lets one throw any sets of (positive or negative) real numbers in the equation at it and get a valid answer. Nifty... PS: If you run into having a square-root of a negative number you can seperate out a negaive 1 and square-root both separately. The square-root of -1 is the imaginary number symbol, usually either small case "i" or "j". Since that only happens here for the part that is added and subtracted to -B/2A; writing that into an answer is pretty simple. Just keep them seperated and add the symbol after the imaginary value. I've never used the Quadratic Equation in electronics, that I can remember. Yet the use of the imaginary number is very common once you start simulating circuits with capacitors and inductors in them. The imaginary part is the out of phase current that is caused by the way energy is stored and later returned to the circuit.
It's really easy to fall into the trap of thinking about a problem in only one way. It's sad our educational systems, even higher education, focus more on rote memorization of cookbook methods, rather than teaching students to reason their way through problems from a solid understanding of fundamental principles. It's even worse in engineering.
@@jessstuart7495 I disagree. Common core isn't rote memory or practice but trying to understand math. You can't just learn math by understanding but by doing.
@@jessstuart7495 I don't know what Autonomous was smoking there because you are 100% correct. Our education systems are so archaic and so filled with bureaucracy that it hurts those that have to suffer through it. Like "Oh you'll learn this next year" or "You should have learned this last year", teachers not knowing the concepts enough to explain them, and a disconnect on what is taught and how things are taught. I had to spend most of my early days in college going back and filling in gaps that I didn't even knew existed because of how poorly the concepts were taught in previous years.
Well, the comment section here certainly turned me off today’s “mathematicians” everyone is so full of themselves. He is a coach for the math Olympiad for god sakes and you are all acting like you know it all and better than him. Thanks to 3 blue 1 brown for sending me here
@@yashuppot3214 The video itself says at the bottom near the end (known for hundreds of years by a) Thousands of years by (b) So don’t pat yourself on the back just because you are so brilliant to realise this
Nice to reconnect! Through this video, I hope to share this beyond who can be reached through in-person presentations, so to leave a lasting improvement in the way people learn how to solve quadratic equations.
The guy only got attention because he is a member of the Church of Academia - a bunch of orangutans who can't accept correction to their flawed ideas. Nothing in his video is remarkable - it's all old news. thenewcalculus.weebly.com studio.ua-cam.com/channels/lBbBVLs3M-d3dNgU4Vop_A.html
I am AMAZED BY YOUR WAY, SIR! I tried to think of most equations, from graphs (not too much complex, though), but I still am amazed that I have missed such a beauty! (The point of the roots being equidistant from a point)(which should have been evident from graphs😅)
It's interesting how various aspects of math get re-popularized at some point in the future. This kind of reminds me about the whole eigenvector thing that came out of the researchers who were looking into neutrinos. They didn't actually rediscover a new eigenvector/eigenvalue identity, but what they rediscovered was so obscure, the leading mathematician Terrence Tao said he has never seen it before. The cherry on top was that the identity the physics researchers discovered perfectly described the phenomenon they were looking into. The humbling aspect was that Tao came up with three proofs for the identity in several hours. Learning new ways to do basic things is probably the most humbling aspect of math. It reminds me that there is always more than one way to do a problem, and that certain methods are truly unique/ingenious. I also like how transparent the proof for this method is, it almost explains itself.
Terry Tao's blogpost: terrytao.wordpress.com/2019/08/13/eigenvectors-from-eigenvalues/ ArXiv post from the three physics researchers arxiv.org/abs/1908.03795
graphically, x=S/2 is the line of symmetry of the quadratic equation, which is why the solution makes sense This method only works if there is a line of symmetry. A huge assumption is already applied when you take the average of the roots and then +/- it. You cant apply this to cubic equations directly at the very least.
If you haven't already realised, your quadratic formula only works for the special case of A=1. School students in the UK have to solve come complicated cases where where A is greater than 1. That's why they use the formula. The general form of your equation is more complicated than the original quadratic formula so not much use.
@@chunjie01 It explicitly says quadratic equation though, why bring up cubics? Interesting video, but this is only for middle schoolers to help them understand the abc formula, because this actually is the abc formula but dressed differently.
One still has to remember that the sum of the roots is -b/2a and their product is c/a, so I'm not convinced this method gains anything over just knowing the formula. But hey, I'm sure there are folk out there who would find remembering this expression of the formula easier.
Any time you have an intuitive method that doesn't require memorizing any formulas is an improvement. I'll never forget how to do this. I did forget the formula and had to look it up.
I've always loved your enthusiasm and positive approach to Mathematics. I'm so happy you intuitively worked out a better way to do something. I hope this will be taught in schools as the new method.
Can people please stop saying "is this a joke??" Or "I knew this already". Most public schools do not teach this method we are taught to use trial and error to figure out the answer, as is stated in the video. Just because you happened to learn it at one point or another does not mean the rest of the world did. It's so hateful to comment things like that when this method is extremely useful to people like me who haven't learnt it, and this man is clearly passionate about his work and excited to share his method. I loved the video and thank you, this simplifies it without having to input numbers into a calculator
@Ice Revenge Thanks for your remark. However, my goal was to show that you don't need to memorize a pq-formula. You can just think through every step. Unfortunately, many people don't know or remember why the pq-formula is true. My goal was to let everyone understand mathematics through thinking, instead of relying on memorization without understanding. In this century, it is becoming more and more important to be able to create our own logical methods, because we have more and more powerful machines that can help us perform routine tasks. On the other hand, if you have seen a textbook which shows this same method of thinking through how to factorize a quadratic, I would be very interested. One of my goals with this video was to seek out previous published references. Please share a link to it, with the title, author, and specific page number, so that we can look on Google Books or Amazon for it. Thanks!
I don't see what is so great in this, I have been using this process much before he 'discovered' it. In fact, in 2017 when I first learnt to solve quadratic equations, my teachers taught me this method before teaching the Quadratic formula.
Recognizing that the roots must be equidistant from their average is not a super obvious thing to think about. After hearing someone else suggest it, it might seem obvious. But coming up with it yourself requires some degree of creativity.
@@KerryKworth or they have absolutely no idea what the formula is actually about (like me) but just know we can substitute the values and grab the solutions
This Is Awesome! And by see, I mean, it literally inspires awe! As a high school teacher, I've always hated the guess and check strategy. It basically makes students feel like they're either really good or really bad at guessing. And that leads to feeling like they're just "bad" at math. This method is incredible!
People, try to get this comment to the top. If the sum of the roots becomes an odd number, it will be really hard to complete this with the method he just taught. Just go with the quadratic formula. Please.
@@GMPranav yes, the complex roots are a bigger problem. Once you do the product as he says, you'd understand it's complex. Yeah I'd do follow this method because i know how i can go wrong, but only if i forget the quadratic formula, that's not happening. Because I've solved almost 1000 equations, again and again no matter how big it does with the quadratic formula.
@@GMPranav I'd never guess. No matter how easy someone finds it, no. I'll use the quadratic formula, confirm it myself, move on. The extra 30-40 seconds i take, but lol idc about that
This is how Dr po shen loh proves one can still become what they want and one can still do new astonising discoveris accidently. You just need the intention and most importantly the passion for it. Thank you Sir. Now I dont have to remember that murderous quadratic formula.
This could be supplemented for teaching by thinking about it graphically, too. As a parabola, the mean of the roots is equivalent to the axis of symmetry (h = -B/2A), so the u term is the distance of the roots from the axis of symmetry. The production of an "exciting lone z² " works out conveniently because the 'linear terms' cancel in the product of the sum and difference of an unknown and a constant, and C is the product of the roots (where A = 1), which are parameterized here as the sum and difference of an unknown and a constant, which is the same as representing two unknowns as their differences from their mean (because the roots are equidistant from the extremum (the X-intercepts are equidistant from the vertex and axis of symmetry)).
Yes! The goal is not to strip away mathematics, but rather to provide alternative perspective. Math is richer than just calculating with memorized formulas. I hope that this helps to provide an intermediate stepping stone that students can walk to right after factoring, which eases them into a logical world of math.
Brilliant❣️..All hear watching video..u all can go through vedic mathematics Which was available 1000 of years ago originated from INDIA🇮🇳💯..U will be mesmerized by the work✌️
Life is only beautiful while studying maths.This makes every student to enjoy to solve maths problems.Because while solving those sums your time is consumed in guessing the numbers .But with this we can actually solve even faster than before .Thanks for your worthy efforts.
Thank you so much for sharing your this. I am from India and preparing for IIT JEE entrance exam and this will help me a lot as the syllabus consist of a major part of the quadratic equation. This method will help me to crack the exam as or is one of the most difficult exam in the world because 1 million students give this exam and only 10k are selected. Thx again
@@zainabrizwan6420 jab koi quadratic equation factorization se solve nahi hota toh sreedhar acharya use hota hai jo vedic maths me tha ho sakta hai tum isko use karte ho bt yeh wala naam nahi pata
Erik l In some tests it’s clear that they are going to give you an easily factorisable quadratic based on context. If 10 year olds have a non calculator exam they can pretty confidently assume every quadratic will have integer solutions
The Indian mathematician Brahmagupta (597-668 AD) explicitly described the quadratic formula in his treatise Brāhmasphuṭasiddhānta published in 628 AD,[24] but written in words instead of symbols.[25] His solution of the quadratic equation ax2 + bx = c was as follows: "To the absolute number multiplied by four times the [coefficient of the] square, add the square of the [coefficient of the] middle term; the square root of the same, less the [coefficient of the] middle term, being divided by twice the [coefficient of the] square is the value."
hey, this is a cool way to intuitively justify the quadratic formula! I feel like I've definitely seen something similar to this in high school (before 2019), although more as a derivation of the quadratic formula from the method of completing the square (i.e. applying completing the square to the full, general form of a quadratic to achieve the quadratic formula) than as a distinct way to solve quadratic equations. I still might argue that it is better to teach students with an emphasis the derivation of the formula, in terms of "how do we get from the general quadratic to something where we can complete the square in general terms, in order to derive a general formula", as it will allow rederiving the quadratic formula any time it is necessary, in a manner as simple as using Dr. Loh's method on any other equation, and also encourages practice in deriving a general formula for a specific procedure, which is a far far more valuable skill than just the ability to solve a quadratic equation.
@@jessstuart7495 well said. More surprisingly, in this case the Babylonians already come up with that variable substitution too, over 2000 years ago! I only noticed that you can combine that with the factoring method that everyone does by guess-and-check in the textbooks.
Felicitaciones apreciable Investigador Matemático Po-Shen Loh por su valioso aporte, que no dudo que formara parte de los currículos de enseñanza a nivel mundial. Mis aplausos para usted respetable Matemático Po-Shen Loh. Atentamente Prof. José Natanael Cortez Rodas, deseándole éxitos en toda su vida personal y profesional.
To check whether his discovery was "new" or not. Usually, once a discovery is wrongly attributed it remains wrong forever - he definitely wanted to avoid that because that is what humble people do. They don't care about fame but the results.
Tbh, this trick is pretty neat but it has its own drawbacks. For example I started with the equation: x² - x - 156 = 0. ( x = 12, -13) By following the same method: Product: -156 Sum: 1 Average value: 0.5 Plausible values of x: 0.5 -u, 0.5 +u .•. 0.25 - u² = -156 u² = 156.25 ......(i) u = ± 12.5 Hence x = 12, -13. I did get the answer using his method, but coming back to eqⁿ (i) you can see that I got a number that is a bit complicated 156.25 . Finding square roots of such numbers is another nightmare. Had I used the splitting the middle term where you prime factorize the product and apply a bit of trial and error, it would've been much more easier. Hence, the method is pretty solid but it's not feasible to use it every single time considering the fact that middle/highschool school kids generally get questions where the numbers are easy to guess.
Thank you Einstein, of course it gives the same result as the quadratic formula, it would be a problem if it didn't... The point is, with his method you get to the solution much faster. Exemple : For x^2+6x+7=0 we can immediately write 9-u^2=7 and then x= -3+-sqrt(2). Done !
It is real he stole everything from ancient Indians and he's actually taking credit for it Many people already knew about this stuff but schools dont do it because they dont want their students to become lazy and think very little
Thank you for sharing this method. I will share it with colleagues and students as it is more transparent than the quadratic formula, which in turn is derived from completing the square. True that ancient peoples had different methods, but I like the way you synthesize it all. Always interesting to read comments from people who "already knew this" yet they never posted a video about it... I appreciate you energy and enthusiasm, well done!
Quadratic formula is different! It's derivation is different, we separate our variable in the quadratic formula and express it in the form of the coefficients and constants of the equation. Where as here we basically make the middle term splitting easier!
I studied Mathematics at The University of Waterloo. This reminds of a technique used in the course, Theory of Interest (Actuarial Science 231), where you learn how to solve infinite and finite series from a Present or Future Value perspective, where one of the often repeated techniques when you have the series that you are interested in, is to create another series and subtract the two, to find a more simplified pattern that pops out - you can then do it again to find further simplification, but effectively, this is what you are doing with this method. When presented with two problems, it is often easier to create a second equation and first solve the first problem, which makes the answer to the second problem automatic. This is a technique that was used constantly in this course and once you see it in action, it becomes almost magical and it will be a goto tool that you will always use. When you study Actuarial Mathematics, the field is littered with these types of techniques that were invented in the pre-computer age, to solve much more complex sums & series, but this 'type' of technique, is rampant in the field. As an aside, because of techniques like this, this course at The University of Waterloo, was by far, the most useful course in Mathematics that I ever studied.
I can't believe it slipped through our eyes for so many years, and now it makes sense. I'm no one I'm just a student but... This was there, all along! It can actually be derived using the quadratic formula... I mean we had ax^2 + bx + c =0 x=(-b +- (b^2 - 4ac)^0.5)/2a This basically means removing the coefficient of x^2, and dividing the coefficient of x by 2, adding and subtracting a value of let's say u Which will be equal to u = ((b^2 - 4ac) ^0.5) / 2a (comparing u to the quadratic formula) Which can be reverse calculated to get ((-b/2a) + u).((-b/2a) - u) = c/a WHICH IS EXACTLY WHAT HE IS DOING!!!!!!!!!!!! How did this slip through our eyes for so long... You can even prove the quadratic formula by using this method!!!! :O
@@hasnainanis193 YEA! And you don't have to search, just make up any quadratic equation, divide it by coefficient of x^2 and apply this method, also make sure that it's the negative of b/2a.
I can remember solving quadratic equations back in high school. I no longer recall how I did it, it was 45 years ago . . . Your method is very clean. Good post! I suppose that I ought know this, but have wondered what real life problems q equations are meant to solve for? That is, supposing we derive the correct answer, what was the question?!
Problems involving acceleration (like gravity) and two dimensions (ex: unknown dimensions for specific areas), plus their are more complex problems that can often be simplified because they include a quadratic.
Sir what if the sum is not an even integer i.e. when it is odd integer then how we'll take the average. Or just simply we can multiply by 2 and make the sum even????? Plz reply??
(For General People)The background will help you to increase fantasy. Maybe you are passionate about Mathematics that's why music annoys you. But it's not true for all people
@@rashedulislamseum7936 I also found the music annoying, it interfered with my ability to really hear what he was saying. It just needs to be at a lower volume, more background, less in your face.
Thanks for sharing your experience. Did your Geometry teacher have a textbook or UA-cam video that showed this method? If so, could you please share a link? One purpose of this video is to seek all previously published work that shows this method. Thank you!
Po-Shen My teacher showed me the method when I stayed after school for a club and asked her about factoring quadratics. Now that I think about it, I’d never seen the method used in any textbooks. Maybe she learned it while in college? Sorry, hope this helped.
@@iflashlantern4292 Thanks for the context. It is helpful. It would be very valuable to find a published reference though, to see how the details were handled. You had a great geometry teacher!
Thank you thank you so much, you don't even after my graduation I'm having problems in guessing the numbers and end up unsolving the question, You just saved my life. Love from 🇮🇳 India!!!
So how would one use this method to factor: 6x^2+x-12 = (3x-4)(2x+3)? I know it's possible, but I can't see it being all that much easier than just manually factoring it by analyzing it. The 'normal' way just seems more obvious and intuitive to me. Not that Dr. Loh didn't come up with an interesting meld of graph observations with algebra, but I really don't find it all that useful.
When you practice solving quadratic equations by factoring, you can usually tell in 3 seconds the combination of numbers required to produce linear factors.
I enjoyed seeing your interpretation of solving the quadratic equation and as it makes total sense. I also know your goal is to simplify this so kids can better understand this but I’m concerned down the line this will hurt them more help them. Out of my experience tutoring intermediate alg and precalculus for college students a lot of them will confuse older topics and how they are done with newer topics. As well when you start to introduce square root principle and more it may be alittle overwhelming at first. To people who are doing math it’s easy but I remember back when I was younger I couldn’t grasp why everything was happening and maybe it was fault on the teacher but it’s still something I never got an answer to until the very end of my high school career. As well I wouldn’t say it’s much of a guessing game when factoring an quadratic equation if you know what every sign is telling you to do and you know how the numbers add and multiply through everything is cake walk till alittle further down the line when you dealing with numbers outside but never the less I think we have a good way of teaching it. We need teachers who are wiling to be patient and promotes staying after school for extra help when it’s needed(it’s what I tell the professors to do)and not only that but I school system who isn’t trying push test out the wazoo and wants kids to learn and not just “get by”. And the other side must do the same. If kids knew how cool math is and how it applies to our real world you’d see kids wanting to learn more. Yes as a sophomore in college I’m learning now that everything in math plays some role wether you see or not; it’s being used for you or against you.merry Christmas btw!
I'm going to use this during an ODE exam and blow my teacher's mind
Update: She did not care
:)
same here
@washboat Buddy, I hate to inform you that almost all of your mathematics educators are idiots who have never understood the concept of number, never mind mathematics.
I am a real mathematician and educator.
studio.ua-cam.com/channels/lBbBVLs3M-d3dNgU4Vop_A.html
Hello @@NewCalculus
This video is for you as you call yourself a true mathematicians
ua-cam.com/video/4sJY7BTIuPY/v-deo.html
This is how the eqution was proven.
Me using this method..
Teacher: well yes, but no...
Why no? This is make sense...
Zia Ihsan yeah but some teachers don’t like creative thinking
PEOPLE, THIS IS NOT CREATIVE.
this is an easy way for your peasant like brain to process it.
Rad Extrem ok then, some teachers believe that anything that isn’t exactly their way is wrong
@@matteogauthier7750 lol yes
Listening to music made me feel like,
He just cracked code to interdimensional travel.
😂
but he did something that is nearly as important as that
I think someone owes Hans Zimmer a royalty for using one of his compositions haha
But he did solve the equation in a more creative and fun way which could help students. Don't be rude🙄
😂😂😂
*abc formula has left the chat*
😂😂😂
Well but you realise that this trick in fact that formula in disguise.
@@GMPranav Yep, but it is basically easier to grab
@@jofx4051 for beginners yes
@@jofx4051 I can recite the abc formula at any time of the day lmao
Me: Can I use this method in my exam?
Teacher: Do you want to pass the exam or do you want to pass away?
Nice one buddy
😂
Lol... My teacher in math is not like that but my physics teacher it is...
You can use whatever method you want as long as you get the right answer
cheating is also a method.
Video needs louder music, a tracking shot of him climbing a misty mountain in central China, and a lot less time fiddling round on the whiteboard.
Albert Batfinder hahaha I’m from China and I agree
😂😂😂irony
I think he spent more money on make this video than the "The beautiful mind" movie.
😂😂😂😂
and the only point is to present an obfuscation of completing the square, what a bullshit video
The most important part was glossed over so quickly while time was wasted with waffle.
What is the most important part?
@@dlemmuh when he explains how to do it , maybe 🤔
@@levick2412 clearly 🤣
Honestly this video was so random. Seemed more like bragging than anything else.
@@DominicanOps Except it's awesome and I'm definitely going to spread it to my students. People are allowed to brag when they do cool things
This is beautiful. It *is* just the same machinations as the quadratic formula, but as an algorithm, its steps are much more intuitive. You are simply turning an arbitrary parabola into a "unit parabola"
1) set r.h.s. To 0 (set the y component to 0)
2) divide by "a" (scale the parabola to coefficient of 1)
3) find b/2 (average of x component of both roots, center parabola on the x-axis)
4) solve for "u" (hard to put in words, but this "coordinates" the focus with the roots)
It's all just translation and scaling, which is much easier to "get" for us (3+t)-dimensional beings than abstract algebra, especially at a young age.
I'd love to see 3blue1brown animate why this works.
I adore how excited and enthusiastic he is. I hated the process of guessing and checking as a kid stressed out on a test. His method is gorgeous and I can appreciate why it's exciting.
wow this music is extremely unnecessary.
Leo Joey and obnoxiously loud
The music in the “Masterclass” advertisments is very close to this.
Something will happen, all time. Kkkkkk
I agree. I found it so annoying that I stopped the video after two minutes.
the music makes the video seem like a satirical skit
Next time make the music even louder and more distracting
😂😂😂
Happier and with your mouth open! (I hope someone knows where this is from)
@@joshuab7464 "Detective Murphy! Just got here. What's the story?"
haha
The background score can be used in any inspirational movie..
You missed the word "annoying"
G M P no u
@@GMPranav that's your last name
@@nikhilb3880 you tried too hard to make a funny comment didn't you?
@@GMPranav Nah, Why would I waste time for you
Anyways it's holiday season for you people I don't want to be 'annoying'
Merry Christmas enjoy you day
This as a pedagogy for 15 yr olds will be much better for me. It also triggered me to think about how to present when you have an "a" term, and a much cleaner method of deriving the formula.
Most kids just blank stare when I derive via completing the squares and I just end up saying "remember the formula".
Thanks mate!
I was inspired to come up with this precisely because I have received the blank stare from students when I derive the quadratic formula in the usual way. It is nice to hear from a fellow educator. The perspective from the front lines of teaching school age students is something that can only be developed by actually doing it.
@Shyan Kothari Stay tuned - about to launch!
@Shyan Kothari Comprehensive video is up! ua-cam.com/video/XKBX0r3J-9Y/v-deo.html
"Completing the square" is where you loose your class. People are following along and everything is going well and then you say "imagine some random numbers that make this work" and people think its witchcraft.
I feel that his passion is more beautiful than the math that he is passionate about... :)
Ikr he looked so so excited ✨
damn ikr
True*
Thank you so much! I'd been struggling with solving quadratic equations because I'd just be *stuck* trying to factor 2 numbers that add and multiply to two different numbers. This is a comprehensive and easy to understand strategy that I will use from now on!
This is precisely how my math teacher taught me to solve Quads back in the 1980s. Hmm...
Seems familiar now also. It is possible to work up a fairly straight forward working spreadsheet that gives valid results for even cases where the results include imaginary numbers in the results. That lets one throw any sets of (positive or negative) real numbers in the equation at it and get a valid answer. Nifty...
PS: If you run into having a square-root of a negative number you can seperate out a negaive 1 and square-root both separately. The square-root of -1 is the imaginary number symbol, usually either small case "i" or "j". Since that only happens here for the part that is added and subtracted to -B/2A; writing that into an answer is pretty simple. Just keep them seperated and add the symbol after the imaginary value. I've never used the Quadratic Equation in electronics, that I can remember. Yet the use of the imaginary number is very common once you start simulating circuits with capacitors and inductors in them. The imaginary part is the out of phase current that is caused by the way energy is stored and later returned to the circuit.
I'm taking algebra 2 right now. I've never seen this. It might have to do with common core
It’s called “U- Substitution”
Been around forever
Silver Falkon lol that’s also found in integration of functions
Thats how I learned it now in High School
Nothing new here, but I do like his enthusiasm. Sometimes finding the right way to reach a student is all that really matters.
Yeah, this method basically looks at the graph of the quadratic and uses its symmetry to find the roots.
It's really easy to fall into the trap of thinking about a problem in only one way. It's sad our educational systems, even higher education, focus more on rote memorization of cookbook methods, rather than teaching students to reason their way through problems from a solid understanding of fundamental principles. It's even worse in engineering.
@@jessstuart7495 I disagree. Common core isn't rote memory or practice but trying to understand math. You can't just learn math by understanding but by doing.
@@Convexhull210 Sorry, whaaaat?
@@jessstuart7495 I don't know what Autonomous was smoking there because you are 100% correct. Our education systems are so archaic and so filled with bureaucracy that it hurts those that have to suffer through it. Like "Oh you'll learn this next year" or "You should have learned this last year", teachers not knowing the concepts enough to explain them, and a disconnect on what is taught and how things are taught. I had to spend most of my early days in college going back and filling in gaps that I didn't even knew existed because of how poorly the concepts were taught in previous years.
I'm equally frustrated and amazed that I didn't know this before.
Caleb Williams it uses same principle as complete the square?
Me too
ax^2+bx+c=0
Sum of roots, S= - b/a
Product of roots, P= c/a
Quadratic formula :-
x= ( - b+-sqrt(b^2 - ac) ) /2a
x= - b/2a +-sqrt (b^2/4a^2- 4ac/4a^2)
x= S/2 +-sqrt( (b/2a)^2 -c/a)
x= S/2 +-sqrt( (S/2)^2 - P)
S/2= average of sum of roots
Dr.Loh
You had come to our school in India
DPS FARIDABAD
Thank You..
Tumhare school me ek foreign lady teacher hain to sahi kya padhati hain vo?
?? I don't think so
@@adityawadhwa9873 Maybe she is guest faculty. You are in which class?
Class X
Dr. Loh came here some 3-4 years back.
@@adityawadhwa9873 Nice to hear from you! :) I remember visiting your school!
Well, the comment section here certainly turned me off today’s “mathematicians” everyone is so full of themselves. He is a coach for the math Olympiad for god sakes and you are all acting like you know it all and better than him.
Thanks to 3 blue 1 brown for sending me here
Idk he should spend more time explaining dont see how i would use this for o lvl lol seems like a waste of time unless my brain alt f4
Dylan Lim 17 Sorry I couldn’t really understand what you were trying to say there
Good comment ✌️ Good perspective ✌️
Because everyone has known this for ages,
@@yashuppot3214 The video itself says at the bottom near the end (known for hundreds of years by a)
Thousands of years by (b)
So don’t pat yourself on the back just because you are so brilliant to realise this
I was at the presentation where he first revealed this
Nice to reconnect! Through this video, I hope to share this beyond who can be reached through in-person presentations, so to leave a lasting improvement in the way people learn how to solve quadratic equations.
Same too
The guy only got attention because he is a member of the Church of Academia - a bunch of orangutans who can't accept correction to their flawed ideas.
Nothing in his video is remarkable - it's all old news.
thenewcalculus.weebly.com
studio.ua-cam.com/channels/lBbBVLs3M-d3dNgU4Vop_A.html
@@psloh Could you post a video working through some examples?
@@d3vilscry666 It's up! ua-cam.com/video/XKBX0r3J-9Y/v-deo.html
I am AMAZED BY YOUR WAY, SIR!
I tried to think of most equations, from graphs (not too much complex, though), but
I still am amazed that I have missed such a beauty! (The point of the roots being equidistant from a point)(which should have been evident from graphs😅)
It's interesting how various aspects of math get re-popularized at some point in the future. This kind of reminds me about the whole eigenvector thing that came out of the researchers who were looking into neutrinos. They didn't actually rediscover a new eigenvector/eigenvalue identity, but what they rediscovered was so obscure, the leading mathematician Terrence Tao said he has never seen it before. The cherry on top was that the identity the physics researchers discovered perfectly described the phenomenon they were looking into. The humbling aspect was that Tao came up with three proofs for the identity in several hours.
Learning new ways to do basic things is probably the most humbling aspect of math. It reminds me that there is always more than one way to do a problem, and that certain methods are truly unique/ingenious. I also like how transparent the proof for this method is, it almost explains itself.
Terry Tao's blogpost:
terrytao.wordpress.com/2019/08/13/eigenvectors-from-eigenvalues/
ArXiv post from the three physics researchers
arxiv.org/abs/1908.03795
When you are at level 100, so you go back to beat the tutorial in another way for fun.
Truly a math teacher with absolute values
can't tell if serious or just intricate satire
ax^2+bx+c=0
Sum of roots, S= - b/a
Product of roots, P= c/a
Quadratic formula :-
x= ( - b+-sqrt(b^2 - ac) ) /2a
x= - b/2a +-sqrt (b^2/4a^2- 4ac/4a^2)
x= S/2 +-sqrt( (b/2a)^2 -c/a)
x= S/2 +-sqrt( (S/2)^2 - P)
S/2= average of sum of roots
graphically, x=S/2 is the line of symmetry of the quadratic equation, which is why the solution makes sense
This method only works if there is a line of symmetry. A huge assumption is already applied when you take the average of the roots and then +/- it. You cant apply this to cubic equations directly at the very least.
Ye, school's method is still easier
If you haven't already realised, your quadratic formula only works for the special case of A=1. School students in the UK have to solve come complicated cases where where A is greater than 1. That's why they use the formula. The general form of your equation is more complicated than the original quadratic formula so not much use.
@@chunjie01 It explicitly says quadratic equation though, why bring up cubics?
Interesting video, but this is only for middle schoolers to help them understand the abc formula, because this actually is the abc formula but dressed differently.
Awesome! So instead of using the formula, I can just compute (b/2)^2 - c, take the square root of that, and add and subtract it from -b/2!
Oh, wait...
This new 'system' is a joke. I wonder where they published the 'work'.
Thts exactly what i was thinking 😂😂......but its better for kids so tht they could understand it easily
One still has to remember that the sum of the roots is -b/2a and their product is c/a, so I'm not convinced this method gains anything over just knowing the formula.
But hey, I'm sure there are folk out there who would find remembering this expression of the formula easier.
Any time you have an intuitive method that doesn't require memorizing any formulas is an improvement. I'll never forget how to do this. I did forget the formula and had to look it up.
@@GabeSmall that was the intention of this method :)
Yo I feel bad for the professor, he's genuinely passionate about this shit and y'all coming for his ass smh
YOU GUYS HAVE NO I IDEA !! i literally HATED math due to always sucking on finding the roots and i am An Engineer. THIS IS HOLY GRAIL FOR ME !!!
OMG this should be in every math textbook !!!
This is literally the derivation of the quadratic formula AHAHHAHAA
No it shouldn't
Because it can't be used for all quadratic equations
@@hidinguy6289 yaa. like 2x^2 huh ?
Its so simple you wont be able to solve complex problems with this that consists√2 or 3 or any other number
I've always loved your enthusiasm and positive approach to Mathematics.
I'm so happy you intuitively worked out a better way to do something.
I hope this will be taught in schools as the new method.
Can people please stop saying "is this a joke??" Or "I knew this already". Most public schools do not teach this method we are taught to use trial and error to figure out the answer, as is stated in the video. Just because you happened to learn it at one point or another does not mean the rest of the world did. It's so hateful to comment things like that when this method is extremely useful to people like me who haven't learnt it, and this man is clearly passionate about his work and excited to share his method. I loved the video and thank you, this simplifies it without having to input numbers into a calculator
I agree with u.
@Ice Revenge england, the most common method is to guess or use a grid
Ice Revenge i don’t understand why u say that if his formula is b-u2=c, doesn’t look like ur formula.
The problem is this dude selling it like some revolutionary discovery of his own rather than just a cool trick to use.
@Ice Revenge Thanks for your remark. However, my goal was to show that you don't need to memorize a pq-formula. You can just think through every step. Unfortunately, many people don't know or remember why the pq-formula is true. My goal was to let everyone understand mathematics through thinking, instead of relying on memorization without understanding. In this century, it is becoming more and more important to be able to create our own logical methods, because we have more and more powerful machines that can help us perform routine tasks.
On the other hand, if you have seen a textbook which shows this same method of thinking through how to factorize a quadratic, I would be very interested. One of my goals with this video was to seek out previous published references. Please share a link to it, with the title, author, and specific page number, so that we can look on Google Books or Amazon for it. Thanks!
Me: Uses this method in Class and gets the correct answer
Teacher: Wrong.
ax^2+bx+c=0
Sum of roots, S= - b/a
Product of roots, P= c/a
Quadratic formula :-
x= ( - b+-sqrt(b^2 - ac) ) /2a
x= - b/2a +-sqrt (b^2/4a^2- 4ac/4a^2)
x= S/2 +-sqrt( (b/2a)^2 -c/a)
x= S/2 +-sqrt( (S/2)^2 - P)
S/2= average of sum of roots
@@shivamsharanlall672 praise you
@@lukamitrovic7873 thanks...
@@shivamsharanlall672
Quadratic formula :-
x= ( - b+-sqrt(b^2 - ac) ) /2a
Really?
@@ItsVideos must have been a typo for 4ac
I don't see what is so great in this, I have been using this process much before he 'discovered' it. In fact, in 2017 when I first learnt to solve quadratic equations, my teachers taught me this method before teaching the Quadratic formula.
His passion for maths is so infectious
I'm gonna use it tomorrow on my SAT math II test!!! Thank you so much!
Wait seriously. Why the hell did i never think of this
Me too
Recognizing that the roots must be equidistant from their average is not a super obvious thing to think about. After hearing someone else suggest it, it might seem obvious. But coming up with it yourself requires some degree of creativity.
@@MuffinsAPlenty Exactly, you need to know Viète's formulas and derive facts from there. Also, the equation must first be converted to x^2+Bx+C=0.
IQ matters
Are you yash dubey
That nerd kid
This is literally just an abstraction of completing the square
Anyone who does not see b^2 -4ac (a=1) in his method is not really paying attention.
@@KerryKworth or they have absolutely no idea what the formula is actually about (like me) but just know we can substitute the values and grab the solutions
Exactly, that's what I said
This
Is
Awesome!
And by see, I mean, it literally inspires awe!
As a high school teacher, I've always hated the guess and check strategy. It basically makes students feel like they're either really good or really bad at guessing. And that leads to feeling like they're just "bad" at math.
This method is incredible!
OMG THIS IS GOING TO BE VERY USEFULL FOR MY JEE ADV EXAM THANK YOU SO MUCHHH!!!!
I don't believe he can actually read arabic i bet it was just for the shot
He turned the page backwards so yeah.
Alex Gordon he was probably trying to find something idk 🤷♂️. He probably can’t read Arabic
People, try to get this comment to the top.
If the sum of the roots becomes an odd number, it will be really hard to complete this with the method he just taught. Just go with the quadratic formula. Please.
Yeah, forget imaginary roots lmao
Be prepared to be called racist because you speak the truth lmao
@@GMPranav yes, the complex roots are a bigger problem. Once you do the product as he says, you'd understand it's complex. Yeah I'd do follow this method because i know how i can go wrong, but only if i forget the quadratic formula, that's not happening. Because I've solved almost 1000 equations, again and again no matter how big it does with the quadratic formula.
@@Radextremlowspecgamer01 TBH this method is worse than guessing
@@GMPranav I'd never guess. No matter how easy someone finds it, no. I'll use the quadratic formula, confirm it myself, move on. The extra 30-40 seconds i take, but lol idc about that
BuzzFeed and WikiHow combined looks like this.
This is how Dr po shen loh proves one can still become what they want and one can still do new astonising discoveris accidently. You just need the intention and most importantly the passion for it. Thank you Sir. Now I dont have to remember that murderous quadratic formula.
I had spent soo much time during middle term breaking but this will help me save soooomich time, Thank you
Thank you for showing us a new way to solve quadratic equations. This does seem simpler and way more effective. Once again, thanks Loh!
This could be supplemented for teaching by thinking about it graphically, too. As a parabola, the mean of the roots is equivalent to the axis of symmetry (h = -B/2A), so the u term is the distance of the roots from the axis of symmetry. The production of an "exciting lone z²
" works out conveniently because the 'linear terms' cancel in the product of the sum and difference of an unknown and a constant, and C is the product of the roots (where A = 1), which are parameterized here as the sum and difference of an unknown and a constant, which is the same as representing two unknowns as their differences from their mean (because the roots are equidistant from the extremum (the X-intercepts are equidistant from the vertex and axis of symmetry)).
Yes! The goal is not to strip away mathematics, but rather to provide alternative perspective. Math is richer than just calculating with memorized formulas. I hope that this helps to provide an intermediate stepping stone that students can walk to right after factoring, which eases them into a logical world of math.
Brilliant❣️..All hear watching video..u all can go through vedic mathematics Which was available 1000 of years ago originated from INDIA🇮🇳💯..U will be mesmerized by the work✌️
Life is only beautiful while studying maths.This makes every student to enjoy to solve maths problems.Because while solving those sums your time is consumed in guessing the numbers .But with this we can actually solve even faster than before .Thanks for your worthy efforts.
Thank you so much for sharing your this. I am from India and preparing for IIT JEE entrance exam and this will help me a lot as the syllabus consist of a major part of the quadratic equation. This method will help me to crack the exam as or is one of the most difficult exam in the world because 1 million students give this exam and only 10k are selected. Thx again
A method for those who forget what factoring is.
bro yeh sridharacharya formula tha na??
Haan shayad ye log ko ana chahiye india
@@2PLUS2FIVE ye ho ta keya hain
Mein ne to kabi ye nam nahi sunna
@@zainabrizwan6420 jab koi quadratic equation factorization se solve nahi hota toh sreedhar acharya use hota hai jo vedic maths me tha ho sakta hai tum isko use karte ho bt yeh wala naam nahi pata
I’m usually quicker with trial and error but idk I might use this
Same trial and error does it for me but sometimes it's too time consuming lol
edboss good luck with that when the solution is complex
Quick example: z^2 - z + 1 = 0
Erik l In some tests it’s clear that they are going to give you an easily factorisable quadratic based on context. If 10 year olds have a non calculator exam they can pretty confidently assume every quadratic will have integer solutions
Rish who learns quadratics when they are 10?
For bigger numbers prolly
The Indian mathematician Brahmagupta (597-668 AD) explicitly described the quadratic formula in his treatise Brāhmasphuṭasiddhānta published in 628 AD,[24] but written in words instead of symbols.[25] His solution of the quadratic equation ax2 + bx = c was as follows: "To the absolute number multiplied by four times the [coefficient of the] square, add the square of the [coefficient of the] middle term; the square root of the same, less the [coefficient of the] middle term, being divided by twice the [coefficient of the] square is the value."
hey, this is a cool way to intuitively justify the quadratic formula! I feel like I've definitely seen something similar to this in high school (before 2019), although more as a derivation of the quadratic formula from the method of completing the square (i.e. applying completing the square to the full, general form of a quadratic to achieve the quadratic formula) than as a distinct way to solve quadratic equations.
I still might argue that it is better to teach students with an emphasis the derivation of the formula, in terms of "how do we get from the general quadratic to something where we can complete the square in general terms, in order to derive a general formula", as it will allow rederiving the quadratic formula any time it is necessary, in a manner as simple as using Dr. Loh's method on any other equation, and also encourages practice in deriving a general formula for a specific procedure, which is a far far more valuable skill than just the ability to solve a quadratic equation.
I am currently a student teacher and I will be teaching this tomorrow. I like your point of view.
This is going to blow all of my teacher's mind when I solve quadration questions super quick!
I’m sure a lot of people went, “why didn’t I think of that?”
Nope
Didn't
That is usually the case with variable substitutions. Tricky to synthesize, but trivial to verify.
Nope, I figured it out myself when I learnt about the quadratic equation in the first time.
@@jessstuart7495 well said. More surprisingly, in this case the Babylonians already come up with that variable substitution too, over 2000 years ago! I only noticed that you can combine that with the factoring method that everyone does by guess-and-check in the textbooks.
This is beautiful. I hope you will continue your amazing research. So that more people can use the beauty of mathematics to create wonderful things.
you're a good man, i always relied on the formula because i hated factorising, now i can do the way i want it to thank you
This is a small part of the whole quadratic factorising steps, it is very useful for large numbers I thank you greatly
Felicitaciones apreciable Investigador Matemático Po-Shen Loh por su valioso aporte, que no dudo que formara parte de los currículos de enseñanza a nivel mundial. Mis aplausos para usted respetable Matemático Po-Shen Loh. Atentamente Prof. José Natanael Cortez Rodas, deseándole éxitos en toda su vida personal y profesional.
¡Gracias!
It really is an interesting connection of 2 simple, seemingly unrelated, facts. What a discovery!
I don't see how I would be forced to look into ancient texts for this.
I'm sure Euler used the same lamp on his table. LOL..
@@digroot dhanayanad and brhamagupta would like to have a chat
To check whether his discovery was "new" or not. Usually, once a discovery is wrongly attributed it remains wrong forever - he definitely wanted to avoid that because that is what humble people do. They don't care about fame but the results.
imma use this from now on lol. thankfully my teacher is really chill with creative solutions. :)
How can I not like this video? Such an excellent method!
Massive congrats on this Po-Shen Loh
This is, literally, a new discovery which can be applied to every math student across the world. Why has this not blown up?
:)
Once people realize you only have to use a calculator one time, as opposed to twice with the quadratic formula, it may. Hopefully. I love this.
Tbh, this trick is pretty neat but it has its own drawbacks. For example I started with the equation:
x² - x - 156 = 0. ( x = 12, -13)
By following the same method:
Product: -156
Sum: 1
Average value: 0.5
Plausible values of x: 0.5 -u, 0.5 +u
.•. 0.25 - u² = -156
u² = 156.25 ......(i)
u = ± 12.5
Hence x = 12, -13.
I did get the answer using his method, but coming back to eqⁿ (i) you can see that I got a number that is a bit complicated 156.25 . Finding square roots of such numbers is another nightmare.
Had I used the splitting the middle term where you prime factorize the product and apply a bit of trial and error, it would've been much more easier.
Hence, the method is pretty solid but it's not feasible to use it every single time considering the fact that middle/highschool school kids generally get questions where the numbers are easy to guess.
@@vladimirjosh6575 oops, my bad. Corrected that. But the fact remains the same. You still have to scratch your head to find the square root of 156.25.
This is a neat solution that incorporates other interesting algebraic and statistical thought processes.
Another Greek malaka.
@@NewCalculus Ha! Howdy!
ax^2+bx+c=0
Sum of roots, S= - b/a
Product of roots, P= c/a
Quadratic formula :-
x= ( - b+-sqrt(b^2 - ac) ) /2a
x= - b/2a +-sqrt (b^2/4a^2- 4ac/4a^2)
x= S/2 +-sqrt( (b/2a)^2 -c/a)
x= S/2 +-sqrt( (S/2)^2 - P)
S/2= average of sum of roots
Thank you Einstein, of course it gives the same result as the quadratic formula, it would be a problem if it didn't...
The point is, with his method you get to the solution much faster.
Exemple :
For x^2+6x+7=0 we can immediately write 9-u^2=7 and then x= -3+-sqrt(2). Done !
Even if quadratic équations are trivial yet you did a great job man
Everything New u teach is worth appreciation
It's as the saying goes: What is old but forgotten is new once more
It is real he stole everything from ancient Indians and he's actually taking credit for it
Many people already knew about this stuff but schools dont do it because they dont want their students to become lazy and think very little
@@centralprocessingunit2564 credit goes to who submits not who invents
Phenomenal research sir thankyou 3000
*Quadratic Formula: IGHT imma head out*
Lol... Btw r u the real virat kohli?
@@ViratKohli-jj3wj chutiya tu hai jiske gaand jaise khaali dimag me humour nahi jaa raha
Lol no one beats the dhanayanad quadratic formula even this will not ensure u answer of all qyadratic problems but the formula will
@@seekeroftruth7745 it was just a joke bro :)
This means I had a really cool teacher! Been doing this since forever.
Thank you for sharing this method. I will share it with colleagues and students as it is more transparent than the quadratic formula, which in turn is derived from completing the square. True that ancient peoples had different methods, but I like the way you synthesize it all. Always interesting to read comments from people who "already knew this" yet they never posted a video about it...
I appreciate you energy and enthusiasm, well done!
Thank you so much for this amazing method! :D
:)
Thank YOU so much for watching!
that is a great way to solve quadratic.saves a lot of time.
And uses only logic!
@@psloh but I think sri dhar acharya method is better....isnt?
Isn't its just another way to right the quadratic formula 😂😂
yea its just derivation of the quadratic formula nothing amazing
It’s just an intuitive way to remember the quadratic formula
Quadratic formula is different! It's derivation is different, we separate our variable in the quadratic formula and express it in the form of the coefficients and constants of the equation. Where as here we basically make the middle term splitting easier!
@@satyajeetdeshmukh1401 It's not the derivation. That's not how you derive quadratic formula.
Except that you can use the quadratic formula also when the parabola is stretched. So it's better
I studied Mathematics at The University of Waterloo. This reminds of a technique used in the course, Theory of Interest (Actuarial Science 231), where you learn how to solve infinite and finite series from a Present or Future Value perspective, where one of the often repeated techniques when you have the series that you are interested in, is to create another series and subtract the two, to find a more simplified pattern that pops out - you can then do it again to find further simplification, but effectively, this is what you are doing with this method. When presented with two problems, it is often easier to create a second equation and first solve the first problem, which makes the answer to the second problem automatic. This is a technique that was used constantly in this course and once you see it in action, it becomes almost magical and it will be a goto tool that you will always use. When you study Actuarial Mathematics, the field is littered with these types of techniques that were invented in the pre-computer age, to solve much more complex sums & series, but this 'type' of technique, is rampant in the field. As an aside, because of techniques like this, this course at The University of Waterloo, was by far, the most useful course in Mathematics that I ever studied.
Thanks for posting the trick.
Its very simple idea.I know this and I teach to my students as alternative method to skip long calculations..
I can't believe it slipped through our eyes for so many years, and now it makes sense. I'm no one I'm just a student but... This was there, all along! It can actually be derived using the quadratic formula...
I mean we had
ax^2 + bx + c =0
x=(-b +- (b^2 - 4ac)^0.5)/2a
This basically means removing the coefficient of x^2, and dividing the coefficient of x by 2, adding and subtracting a value of let's say u
Which will be equal to
u = ((b^2 - 4ac) ^0.5) / 2a
(comparing u to the quadratic formula)
Which can be reverse calculated to get
((-b/2a) + u).((-b/2a) - u) = c/a
WHICH IS EXACTLY WHAT HE IS DOING!!!!!!!!!!!!
How did this slip through our eyes for so long...
You can even prove the quadratic formula by using this method!!!! :O
I was searching for maths to use this formula on. But i stumble upon this comment. And Crap! It actually solves the quadratic Equation!!😲
@@hasnainanis193 YEA! And you don't have to search, just make up any quadratic equation, divide it by coefficient of x^2 and apply this method, also make sure that it's the negative of b/2a.
We're glad you had an aha moment! And a student is certainly a somebody, not a "no one!" You're so valued, and we're so glad to have fans like you.
And -b/2a is the vertex. Quadratics are symmetrical.
I can remember solving quadratic equations back in high school. I no longer recall how I did it, it was 45 years ago . . .
Your method is very clean. Good post!
I suppose that I ought know this, but have wondered what real life problems q equations are meant to solve for?
That is, supposing we derive the correct answer, what was the question?!
Problems involving acceleration (like gravity) and two dimensions (ex: unknown dimensions for specific areas), plus their are more complex problems that can often be simplified because they include a quadratic.
Thanks for including Indian Mathematicians unlike others.
Learning is finally fun, this guys a legend, TYSM 😀
I have learned something new (to me) today ! Elegant and simple solutions are always the best.
Excellent!
This is trivial. I don't think this method deserves the extreme, over the top music in the background.
How come?
Fabulous, Brilliant.This is what we call maths....👍
That is beautiful and I will teach it in the next couple of weeks.
Happy to help!
You’re the best Mr.professor Po.
Sir what if the sum is not an even integer i.e. when it is odd integer then how we'll take the average.
Or just simply we can multiply by 2 and make the sum even????? Plz reply??
@Cool Guy You don't need to....if the B is odd just keep it like (B/2)² and go on... you'll find the right result.
Nice video, I find the background music a bit annoying, maybe it interferes with processing of math in my brain.
(For General People)The background will help you to increase fantasy.
Maybe you are passionate about Mathematics that's why music annoys you.
But it's not true for all people
@@rashedulislamseum7936 I also found the music annoying, it interfered with my ability to really hear what he was saying. It just needs to be at a lower volume, more background, less in your face.
very silly comment
@@franciscochaparro-torress5010 Very silly you.
But it's so much more dramatic and intense with the music. It makes it sound epic and epiphanic
My geometry teacher taught me this 3 years ago and I never knew people didn’t use this all the time.
Thanks for sharing your experience. Did your Geometry teacher have a textbook or UA-cam video that showed this method? If so, could you please share a link? One purpose of this video is to seek all previously published work that shows this method. Thank you!
Po-Shen My teacher showed me the method when I stayed after school for a club and asked her about factoring quadratics. Now that I think about it, I’d never seen the method used in any textbooks. Maybe she learned it while in college? Sorry, hope this helped.
@@iflashlantern4292 Thanks for the context. It is helpful. It would be very valuable to find a published reference though, to see how the details were handled. You had a great geometry teacher!
You deadass had a great Geometry teacher. By God I never knew about this.
Idris Khan other kids in my same school never knew about this. Pretty crazy how much we sometimes take for granted.
Thank you thank you so much, you don't even after my graduation I'm having problems in guessing the numbers and end up unsolving the question,
You just saved my life.
Love from 🇮🇳 India!!!
So how would one use this method to factor: 6x^2+x-12 = (3x-4)(2x+3)? I know it's possible, but I can't see it being all that much easier than just manually factoring it by analyzing it. The 'normal' way just seems more obvious and intuitive to me. Not that Dr. Loh didn't come up with an interesting meld of graph observations with algebra, but I really don't find it all that useful.
At least this video said “different” way, not “new” way. The title saved it from having my dislike.
In a lot of articles it is emphasized that it is not a new way
You can always use QUADRATIC FORMULA !!
If
[aX^2+bX+c=0]
[X={-b+-√(b^2-4ac)}/2a]
FOR GOD SAKE !🤣
@@owenwalters1 Read clearly what he wrote then comment
@@owenwalters1 Yes I stopped doing it, just like you. Now we can talk
No it didn't?
Lol! In Indian schools this is taught to students in grade 8 as a standard method along with the other two(the formula and graph)😂
Ye same bro
Yes in germany too
Could you post a link or two? I was trying to tell my friend the same. Thanks.
ps seems to me the assumption that the roots are (1/2) B +- Z is .. equivalent to completing the square.
Jhoot mat bolo, 8th me ICSE me padhate honge CBSE me nahi (Though lot of students know about it in class 8)
When you practice solving quadratic equations by factoring, you can usually tell in 3 seconds the combination of numbers required to produce linear factors.
Ya. But don't think like that. İf they about 3-✓5. This solving is good for them.
He actually explains in another video that he found it satisfying to not rely on testing out all linear factors.
Yes, if you have mental math skills, which most Americans do not possess
@Catherine Bickford No matter how large the number is, I have come up with a formula for obtaining the two factors
That's because the problems are designed to have nice integer solutions. This does not require that.
Professor.I'm watching the video.
your level of enthusiasm baffles me.
I'm a beginner.I love combinatorics .What's the best way to learn it pls?.
I enjoyed seeing your interpretation of solving the quadratic equation and as it makes total sense. I also know your goal is to simplify this so kids can better understand this but I’m concerned down the line this will hurt them more help them. Out of my experience tutoring intermediate alg and precalculus for college students a lot of them will confuse older topics and how they are done with newer topics. As well when you start to introduce square root principle and more it may be alittle overwhelming at first. To people who are doing math it’s easy but I remember back when I was younger I couldn’t grasp why everything was happening and maybe it was fault on the teacher but it’s still something I never got an answer to until the very end of my high school career. As well I wouldn’t say it’s much of a guessing game when factoring an quadratic equation if you know what every sign is telling you to do and you know how the numbers add and multiply through everything is cake walk till alittle further down the line when you dealing with numbers outside but never the less I think we have a good way of teaching it. We need teachers who are wiling to be patient and promotes staying after school for extra help when it’s needed(it’s what I tell the professors to do)and not only that but I school system who isn’t trying push test out the wazoo and wants kids to learn and not just “get by”. And the other side must do the same. If kids knew how cool math is and how it applies to our real world you’d see kids wanting to learn more. Yes as a sophomore in college I’m learning now that everything in math plays some role wether you see or not; it’s being used for you or against you.merry Christmas btw!