Learn how to solve Quintic Equation (x^5)-(x^4)-(x^2)-=(5x^3)+6x quickly | Math Olympiad Training

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Learn how to solve Quintic Equation (x^5)-(x^4)-(x^2)-=(5x^3)+6x quickly | Math Olympiad Training

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solve Quintic Equation (x^5)-(x^4)-(x^2)-=(5x^3)+6x

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[davidfromstow]

Most enjoyable - you always make it seem so easy! Thank you

[ignacy]

Thanks for uploading these kind of videos. I am from Poland and someday I want to win the Polish Math Olympiad. You're so helpful,

[Mete_Han]

Here is another question whose solution is more super than the question, thank you PreMath

[parikshitparekh]

Quick revision of last year Maths for me
Thank you!

[j.r.]

When you reach the fourth-degree polynomial, it also can be factored just by rearranging the terms: x^4 - 5x^2 - 6 - x^3 - x. The first three terms can be factored as a group, and so can the final two terms. The common factor is then (x^2 + 1). This is how I did it.

[SuperYoonHo]

thanks so much friend the solution made me say wow!

[owlsmath]

Good problem! Thats some tricky factoring maneuvers

[alster]

I solved this by using

1.) Rational Zero Theorem
2.) Factor/Remainder Theorem
3.) Synthetic Division

And got the same result

[jrmiduq]

I solved it using the assembly method, but your solution is better than my solution. Thank you for the great idea.

[math]

very well explained, thanks for sharing this quintic equation

[HappyFamilyOnline]

Very well explained👍👍
Thank you so much for your hard work💕💕

[wolframiumlavasioth]

I used Ruffini's rule and got the same results! I was almost certain I did something wrong when I saw I was getting complex numbers, but it was correct!

[jarikosonen]

Factoring looks like hard part.
But it proves that at least some 5th degree polynomials can be solved for the roots.
What is the exact algorithm to factor it? Test all possible cases?

[davidbrisbane]

Of course, it isn't possible to solve the general quintic equation by any algebraic methods. Special cases like this one can be solved by such methods.

[buxeessingh]

Amusingly, I figured out i and -i had to be roots aside from zero. I feel weird. Imagine my shock to discover that the rational root theorem was the easier route.

[mahdiali]

Sir how can I learn minupalution in math

[ChavoMysterio]

I know one the roots is zero. No constant in original equation.

[dutchie]

Rational root theorem would have been useful here.

[facebookatul]

I have solve it within 1 hr 😅 but the ans is same as sir solved