Rational Roots Test / Theorem
Вставка
- Опубліковано 17 лис 2024
- Rational Roots Test - In this video I talk about how you can find all of the possible rational roots of a polynomial.
Note that to find the rational roots of a polynomial we simply look at all possible combinations of factors of the constant divided by factors of the leading coefficient.
Note that if there is not a constant, all terms involve some power of x. In this case FIRST factor out the smallest power of x and then use the rational roots test on the remaining factored polynomial.
Once you have all of the possible rational roots it is just a matter of substituting each candidate into the original polynomial to see if any of these values give zero after simplifying.
#maths #patrickjmt #rationalroots #factorial #polynomials #zeroes #zeroesofpolynomial
I was three year olds when this video was made. Now this same video is helping me 11 years later
Damn bro.
You lookin into this by the age of 14 🤙
@@redumptious2544 fr
Same bruhhh😬
same here
@@redumptious2544 in Ireland we do this at 12
I swear! This man saved me from going insane and failing my Algebra 2 class during the summer! The teacher was so awful. Thank you!
this is such a basic topic
yabang
ya rema
Angel Gongona oo nga po😂
Same here, my pre calc professor sucks. This guy is saving my ass from failing.
at 4:12 you said "you get negative five" but the numbers are 2 and -3, so 2-3-11+6=-6, still not zero, but just clarifying in case anyone else caught that
I have also noticed that, because 2 - 3 is equal to -1.
I NOTICED THAT OMG I JUST SAW THIS COMMENT, weird is that I also put 4:12 👽 very timing
@@troydelantar7899 maybe its just a mis-understanding
he also made a mistake at 5:12
Use the rational roots test and then plug the possible roots back in the polynomial to see if they = 0. Or, like what your professor did use the possible roots and the polynomial in synthetic division. If the remainder is 0 then it's a root. Both ways work but it'll probably be faster to do synthetic division.
You're doing God's work.
lol
LOLL
Foolish!!
No one is like God in any context.
@@ahsanulhaq8056 🧒 CHILD 👶
Man, you explain math better than all of the math teachers that I used here in Bulgaria. Thanks bro!
It seriously annoys me how I learn concepts in under 3 mins on this channel 😂😂
goes through 12 years of math, never hears of this, hears it, is ever so grateful, you sir are a legend!
I think it's not -27-33+6 it should be 27-33+6. Just get rid of the negative sign in 27 .
Andrea Delos Santos thats -27+-33
u r rite
@promas this is misleading information and people will get confused, please correct it. Or further explain it.
@@patrickdeveloper7186 at 5:30, The guy subtract 54 and 27 in the '54-27-33+6'. 54-27 is positive 27, not negative 27. That's why the 27 in his -27-33+6 should be positive. But since he did calculated the 27 as positive despite it visually doesn't, he answered the equation correctly.
54-27= -27 ?????????????
5:31
54-27=-27
-27-33=-6
-6+6=0
Nice for you to help us, but please recheck work. + for the effort
This video is helpin saving my grade in alg 2 rn. Thank you so damn much man. I have no idea when this came out but im so happy this is here!!
Patrick...I love you.. I've been watching your videos for quite some time now, you helped me through algebra, stats, precalc, calc etc..
You sir, are the reason I will pass my math quiz tomorrow.
well did you pass?
U asking after 3 years
@@sureshotshorts1207 sometimes ya just wanna know
Did you pass?
Correct me if Im wrong, isn't it 2-3-11+6=-6?? Not 10? From the first equation u gave.
I was thinking that only I noticed it, made me do a double-take
Same
Unless one of them is suppose to be positive/negative, also remember PEMDAS
Yeah it's -6
U right fam
This guy saved me from failing my Algebra 2 class during this year! The way the Connexus program is so sketchy! Thank you so much!!!
if you are using real numbers, one can not just look at the degree and conclude the polynomial has that many roots.
consider f(x) = x^2 + 4
this has no roots (again, using real numbers).
the degree is the maximum possible number of real roots.
euler (i think) proved that there will be n solutions (some repeated) to a n degree polynomial if we use complex numbers - it was his phd thesis!
You are the best math teacher on UA-cam. Without you, I would have failed so many classes but I have to ask, when will this ever be applied to life?
Exactly what I was looking for
Studying day before major assessment. This is the best vid I found after an hour of looking. Thanks man
I have my test in less than 1hr and from the bottom of my heart thank you so much.
good luck!
Just found your videos thru my college algebra class. You're so much more help than my teacher herself...
glad i could help you :)
I'm sure it's not to important now but he should have used synthetic division to check. it's a lot faster. if you don't know what synthetic division is, look it up, it's very helpful for dividing polynomials
JaxamussAwesomessMaximuss of course he could’ve used it but this is the rational root theorem that he’s trying to teach us (Yh I know this is like 2 years late oops)
@@aneesak-ar-im3869 no such thing as late on youtube bb
Ive heard synthetic divion is very limited
CrimsonKnightmare How so?
You saved my Math grade ,Sir!! Thank you so much for such an awesome video!!
Just to mention, after you have determined the three roots, when you write f(x) you need to include a multiplicative constant factor, which turns out to equal 2. That will give you the function you started with.
Another way to find the roots and factored form of f(x) is that once you have found one root you can divide (syn. div.) by that factor to determine the remaining quadratic, and then factor the quadratic.
Drop a confident reply if you got me today after so many years ❤
Not trying to say Patrick's teaching skills are any less, but part of the supplement to his teach skills is the ability to rewatch and pause his videos to learn at your own pace. This is an added bonus to his skill to easily explain math without using words that are superfluous, as most math theorems do. Thanks so much for helping me out, been watching since 7th grade Alg 1, now am a freshman in Precalc :)
Thank you, so much. Your videos help me with math more than any teacher I've ever had
glad to help!
I think at 6:41 , if you expand the bottom function, it doesn't equal the top function. Instead it equals the top function / 2. If you replace (x - 1/2) with (2x - 1) then it works. :)
.
.
.
.
.
ya
Thank you it made things a lot clearer and connected everything I learned so far
Your videos are a blessing for me during this covid 19 crisis. THANK YOU!!!
I was near 3 months old when this vid was made now it’s helping me after 14 years
yep! i hope it made sense for you : )
At time -1.23 you note that 57-27=-27 and then go on the day that -27-33=-6, just thought I would note that 57-27 is in fact positive 27. Thank for making this video though!
You are really helping me along the path to my math degree. Thanks Patrick!
Superb i am watching it after 11 year
I was exactly 4 months old when this video was made. And now I'm 15 years old and this video helps me.
I was 1 year old when this video was made and now 14years later this video is helping me😀😀
i wasnt ever bornn when this video was made.. then it helped me 13years later thank you
I was overthinking this cause the other videos made it feel complicated. Thanks for explaining it straight on :)
for some reason my math class books and other material teaches weirdly and complicates stuff. This was very helpful!
Be careful when you are adding or subtracting negative signs.
It's actually not -27 but +27-33+6
=0
ohhhh thats why i was confused lol
@@StormForthcoming yeah, you can visit my profile as well but I don't think so if you can understand because I used Filipino language.
Why are you not my teacher, you make it so simple and easy to understand.
Hi all! Please post comments, questions and anything else on your mind in the comment section! Also, don’t forget to LIKE, THUMBS UP, and SUBSCRIBE! I’d appreciate it greatly :)
U put negative 27 even though it's positive
Nope - 3(3)`2 is 27 since 3*3=9 and 9*-3=-27
@@khomchat1 he is taling about 54-27 =27 not -27
Oops looking at the wrong one
Yes, he wrong -27 but he still computed it as positive 27. So no actual error that affected the answer.
But the answer still is correct
Video is 11 years old but still better then my math teacher thanks man!
you are welcome!
You just explained in 6 minutes what my teacher couldn't explain in 30. Thank you.
You explained a lot better than my package of notes.
Thanks!
ufufu
Thank you so much! I had a hard time with figuring out where the fractions came from, but now I know!
Thank you so much! I never knew how simple this type of problem could be and now I can start my homework... before school reopens tommorow...
yes, first factor out the x.
then you can use rational roots thm on the polynomial of degree 6
i was 12 years old when you uploaded this video and now i am 26
Best math teacher on UA-cam.
I wanna take a minute to thank you, for spending time to help me, and everyone else who has seen your videos! Keep making them! :D
OMG you made my life so much easier i have a test in 3 hours... i was gna FAIL thank you thank you thank you keep up the great work :D
Are u alive?
This video helped me explain this concept to my high school students.
@Zen113 what i am doing on youtube is more effective than what i could do in any class room i think.
I wish you were my math teacher.
I mean, I understand everything I needed to understand by watching your short videos than being in a room for an hour and a half!
:)
Theres a faster way to do this which is if it's a cubic (90% of the time it will be a cubic, since those appear more)
1. Simplify as much as possible, make sure there are only integers. MAKE SURE "a" coefficient is positive (Multiply by -1 if not)
2. Try 1 by adding all coeeficients, and try -1 (You only need one root to end this cycle of rational root theorem).
3. If no answers, THEN Take descartes's rule of signs since this works for cubics as it yields 2 possible sets only.
*NOTE: A cubic is depressed if there is no x^2 part.
4a. IF the cubic is NOT depressed Take the derivative and set to 0, then plug the answer back into the equation using a calculator and see which of the de moivre's part is right. If its complex answer there can max be 1 root. If one of the answers yields 0 as y, it means that the equation has a double-root and that is one of the roots. You can synthetic divide and stop here if this is true. If it yields 0 but there is only 1 horizontal tangent, it means there is a triple-root and you have just found all 3 roots (this is super duper rare though)
4b. IF the cubic IS depressed, you can choose to either do 4a or find the discriminant and use that. If the discriminant is above 0 there is 1 real root, below 0 and 3 real roots, equal to 0 and 2 real roots. (Search up how to find the discriminant)
5. Using that info determine which of Descartes possibilities are right.
6. Use #5 and synthetic division and figure out if its below or above zero. If its below zero, eliminate all of the answers below it (unless there is another root, then be careful) and same for if it's above. (If theres another root, the graph can go back the other way again, so it's important to know it). Using this will eliminate like 2-3 solutions every try.
7. IF there is a rational root, find the leftover quadratic and figure out the other roots. (If its 1 real root, there will be 2 complex roots, and if its 3/2 roots there will be 2 real roots.)
8. If there is no rational root, either 1. Die 2. Depress the cubic and use Cardano's formula and die of exhaustion 3. Learn to code and approximate the root. (don't be that guy)
Hopefully this helps, if it's not a cubic then die as well!
i have a video on synthetic division if that helps : )
Do you have one for integer root test/theorem
god bless your soul mister. you have literally just saved me from failing my math class😭😭😭👌👏
bro you rock i learn more math on you tube than in class somtimes
Thanks for teaching me what my teacher didn’t
My Maths teacher sucks at an epic level... Thank u!!! I understood now
thank you so much sir, without you, i wouldn't pass calculus and therefore not be able to get into computer systems classes in college.
dude, thank you very much, next month I will have an entrance exam in mathematics at the Lyceum, and this video helped me understand the topic, thanks)))
its almost 1 a.m. and I have a quiz tomorrow in honors alg 2 on this and I had no idea what was going on until this video. THANK YOU! you accomplished in 6 mins what my douche teacher couldn't in 90 minutes
no, u can always just reorder it
Thank you soo much for this video!! I was so lost but now I understand! Thank you!
I am a linear algebra student who is not allowed a calculator so I am back to the basics for finding the characteristic equation of a 3x3 (not triangular) matrix
the last polynomial should be multiplied by 2, which is 2(x-1/2)(x+2)(x-3)
anyway thanks a lot
You helped me get an A in this chapter, thanks.
Awesome! I am sick and I am still learning the stuff my classmates are in class. Awesome!!
All your videos Such a valuable gift 🎁 for me on youtube .
What am I in school for when you exist?
you are much better than my math teacher!! thanks a lots!!
You are a life saver for my algebra 2 final!
12 years later and still killing the game
thanks so much. helped me tons with my finals!
Are u alive????
u still alive bruh?
Thank you very much you are a very pro efficient teacher!
thank you so much,sir! You're much better than my math book !
Happy to help
You made this very easy. Thanks
If you become an accountant, when will you ever apply chemistry or biology in life? If you become a professional football player, when will you ever apply world history in your line of work? Pretty much everything you learn in school is built to open up more paths for your future and what you will use depends on what you become.
My teacher really confuses me, now I understand thank you.
thank you, my confusion is relieved
Ur 1 of the 2 peoples vids I watch for math, the other is David reneau, but u still do really do it good, since David teaches a class, he makes more clear for me tho
thanks so much for the solution :) I was having a hard time using synthetic division. I'll try doing how he's doing.
This video helped a great deal. Thanks you.
The concept of the rational roots testing makes sense, but factorising that polynomial gives (2x-1)(x+2)(x-3)
Yes I too have the same doubt man
yes, i just need to remake this one later today! : )
didnt know it was uploaded in 2008 but thank you so much for uploading this video
it really helped a lot
this is a really lengthy process, but it’s the only thing i understand so thank you :))
Thanks! My teacher taught this in a terrible way. You are so much help.
thanks man you explained it really well
Shouldnt you consider the negative versions of the possible rational roots too?
What a coincidence, our maths holiday homework had this exact question haha
I'm in algebra three and we never were taught this.
thank youuu ! you simplify things so muchh
Thanks, easy to understand.
this literally saved my life
I got a 40% on my test. Thank you
@aceonx the amount of roots depends on the highest power x factor... so in x^3 + x^2 + x + 4 or something, 3 is the amount of roots, because this is the highest power x factor