I can't thank you more Professor Leonard, I just passed my calculus 2 exam theory because of you and i almost got 100% on it. You are the best, keep it up and thank you for your videos. Joining you on Patreon very soon!
Professor Leonard, thank you for an exceptional video/lecture on Finding All Real and Complex Solutions of Polynomials. Factoring and Synthetic Division continue to play an important role in finding real and complex solutions.
On thing to help too is if you have positive descartes values, all the signs on the exponents are positive, and 1 is too high, you don't need to try any higher values so only the fractions can work. Same for the revers if 1 is too low then only higher numbers can work and the fractions wont.
@@rosepierce9382 I've always been a fast talker, so I guess I'm just used to listening to fast talkers. He talks very slow to me in normal speed, so if I really need to pay attention I still have him at 1.5 speed.
@@scopeless22 I tried doing that, because it'd save me a LOT of time, but ended up going back to normal speed. Oh, well. I am also taking notes, so yeah. Anyways, thanks for replying and hope you have the most wonderful day!
Hi Professor, love your video and a big fan of your channel. I ran into a problem which need your help to shed some lights on it. For polynomial y=x^{4}+22x^{2}+50x-25, Desmos graph calculator shows it has 1 negative (-2.255,0) and 1 positive (0.421,0) and 2 imaginary solutions, but rational number solutions are not the factor of p/q 25/1 (plus minus, 1, 5, 25 etc.), is there a reason why rational zeros theorem does not work for this polynomial?
Professor Leonard mentioned two videos ago that Descartes’s rule may not supply all the multiples, especially when you use the quadratic formula to factor. I am not sure the underlying reason though.
Professor Leonard, I have a question about Descartes's rule of signs. If you run f(x) for the equation it says that we will either have 3 or 1 positive x-int. And if you run f(-x) for it then you have 1 negative x int. Am I correct or is there something that I am not looking at?
@@saljimenez7071 Yes we have either 3 or 1 positive X intercept while only 1 Negative X intercept.... after getting the solution that gets validated x=5 and x=-2 are the + and - x intercepts respectively..... rest being irreducible quadratics never touches the X intercept.... Appreciate you brother ... try to incorporate previous points so that we will never miss those ideas ...
I can't thank you more Professor Leonard, I just passed my calculus 2 exam theory because of you and i almost got 100% on it. You are the best, keep it up and thank you for your videos. Joining you on Patreon very soon!
When are you going to teach us your workout routine??
Professor Leonard, you are my biggest inspiration in life, buff and smart!
🤫
Lots of love from India. Sir. M in love with ur teaching techniques.
Honestly thank god for you. There's no way I'd be able to understand this by reading from a textbook.
You're a terrific teacher, thanks for all the help and for the free material.
Professor Leonard, thank you for an exceptional video/lecture on Finding All Real and Complex Solutions of Polynomials. Factoring and Synthetic Division continue to play an important role in finding real and complex solutions.
On thing to help too is if you have positive descartes values, all the signs on the exponents are positive, and 1 is too high, you don't need to try any higher values so only the fractions can work. Same for the revers if 1 is too low then only higher numbers can work and the fractions wont.
Thanks for the lessons, sir.
Waiting patiently for trigonometry!
Those who watch this channel often any good channel to learn trigonometry in full.
there are no good channels for trig unfortunately. I also am waiting on prof Leonard haha
Thank you sir.
Please do some more differential equations videos
Thanks
This is very helpful, thanks!
20:30 onwards
Holy...shit. So that is why its called LONG division!
you are the BEST
Please make a Delta-Epsilon definition of limit
Yeah I also want it...
love you
How do we interpret complex roots of a non-quadratic polynomial graphically?
45
Ive been watching these at 1.75 speed and just realized that now I'm used to his faster higher pitch voice and his normal voice sounds weird.
How do you do that and still understand everything he says? I lose track very quickly.
@@rosepierce9382 I've always been a fast talker, so I guess I'm just used to listening to fast talkers. He talks very slow to me in normal speed, so if I really need to pay attention I still have him at 1.5 speed.
@@scopeless22 I tried doing that, because it'd save me a LOT of time, but ended up going back to normal speed. Oh, well. I am also taking notes, so yeah. Anyways, thanks for replying and hope you have the most wonderful day!
@@scopeless22 THE EXACT SAME THING HAPPENED TO ME TOO 😂
You can use synthetic division with complex numbers. Is there an advantage of not doing it that way?
I come here to click like first (as working in the morning), later at night will watch this video.
Hi Professor, love your video and a big fan of your channel. I ran into a problem which need your help to shed some lights on it. For polynomial y=x^{4}+22x^{2}+50x-25, Desmos graph calculator shows it has 1 negative (-2.255,0) and 1 positive (0.421,0) and 2 imaginary solutions, but rational number solutions are not the factor of p/q 25/1 (plus minus, 1, 5, 25 etc.), is there a reason why rational zeros theorem does not work for this polynomial?
Professor Leonard mentioned two videos ago that Descartes’s rule may not supply all the multiples, especially when you use the quadratic formula to factor. I am not sure the underlying reason though.
"because what i is is imaginary" 😂
june 14 2022
Professor Leonard, I have a question about Descartes's rule of signs. If you run f(x) for the equation it says that we will either have 3 or 1 positive x-int. And if you run f(-x) for it then you have 1 negative x int. Am I correct or is there something that I am not looking at?
im am speaking about g(x)=x4-9x3+21x2+21x-130
@@saljimenez7071 Yes we have either 3 or 1 positive X intercept while only 1 Negative X intercept.... after getting the solution that gets validated x=5 and x=-2 are the + and - x intercepts respectively..... rest being irreducible quadratics never touches the X intercept....
Appreciate you brother ... try to incorporate previous points so that we will never miss those ideas ...
Can you make something on pure mathematics? It would be just great😍
Thats a pretty vague question.