Fundamental Theorem of Algebra

This math video tutorial provides a basic introduction into the Fundamental Theorem of Algebra which states that a polynomial function of degreen n has exactly n roots provided that n is equal to or greater than 1.

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[stephenwood]

This presentation is a model of clarity and methodical presentation. Very, very good stuff. This is a public service. Thank you.

[Frirkrkkoii]

One of the best teachers in youtube, I learned a lot from you man, keep up the good work 👏 ❤

[georgesadler]

MR. Organic Chemistry Tutor, thank you for a fantastic explanation of the Fundamental Theorem of Algebra. Once again the Playlist is exceptional from beginning to end. Algebra is very important in all levels of Mathematics. The impact on students worldwide is off the learning and educational charts.

[amberwalters]

You have always explained things so simply. You've helped me so many times while homeschooling my daughter.

[shepherdpchibanga]

Thanks so much for what u are doing you are teaching and motivate me . I was poor in Mathis but now I don't have

[ernstboyd]

Id like to offer some intuitive understanding for why a cubic equation has 1 or 3 real roots
if x is a large positive number then the x^3 term will win out and make the polynomial grow larger and larger
(assuming the coefficient for x^3 is positive)
if x is a negative number far from 0 (a large negative) then the polynomial will become negative more and more.
so it has to cross the X axis at least once
It may also cross the X axis 3 times so it has 3 roots
the other possibility is that it crosses once and the comes back to the X axis and brushes it like the parabola y=x^2
when it does this brushing it counts a two roots that just happen to be the same because its like crossing it once
and then soon crossing it again
Its also possible that the curve crosses the X axis momentarily stoping on it like y=x^3 does (called an inflection point)
and this is where there are 3 roots that just happen to be the same.
a similar argument can be made for 4th degree polynomials to understand why they have to have 0, 2, or 4 roots
(again the roots may join as brushing and inflection points if they happen to be together)
and the same for 5th degree ...

[klips]

Could you make a video about logic, arguments and validity, Quantifiers & rules of inference?(love ur videos teacher)

[utilizator]

I think this theorem is used to demonstrate that if a process has z_+ unstable zeros (in control engineering, if you have a transfer function H(s)=B(s)/A(s), where A and B are polynomials, the zeros of H are the solutions of B(s)=0), its step response y(t) will intersect y(0) orizontal axe z_+ times.

[TheChainsbroken]

Thanks for your passion to share awesome content.

[Mr.Wick]

I feel like im in school again 😊. Great explanations, makes it a lot easier

[Awesome奥深]

Cool, the sound clear, and understandable.

[shyaamsundar]

Nice concept video!! I love u man !! Ur a best teacher who I have never seen !!

[umarabbas]

Thank you sir once again, you are a true lagends

[wingsoffreedom]

Plz could u make a long video on matrix, determinant, cofactor, transpose of matrix

[annabellethedoll]

Hello Mr. Julio, are you considering making abstract algebra, if you haven’t?

[NiharikaPandey-sr]

According to fundamentals theorem of algebra about the no. Of roots for any polynomial of degree n

[katelynleblanc]

hey tutor! can you do to way frequency tables. i've been struggling a lot with it it class and it's very confusing! i would appreciate it if you did a video on it. your the only person i genuinely learn from

[jamesruz]

wish i had this video when i was in the 7th grade lol

[electivire]

Does anyone know what software he uses for the notes?

[abdullahsaed]

hello my hero can you please teach us static course please