a very simple equation

Algebra Level 2

if X is the sum of the roots of $x^{10}-9x+8=0$ , then what is the value of $X^2-5X+7$ ?

The answer is 7.

2 solutions

Michael Fischer
Sep 10, 2014

Given, X = the sum of the roots of $x^{10}-9x+8=0.$

By Vieta's Theorem, that sum is the coefficient of $x^9$ which is zero.

So X=0, and the value of $X^2-5X+7\text{ is 7}$

Hmm.. actually the sum of coefficients in a quadratic equation is -b/a.. but I see that the coefficient of power 2 is zero and thus a=0 and b=-9...so it will become -(-9)/0 which is not equal to zero but is not defined..... So how can X be equal to 0 ?

Parag Zode - 6 years, 9 months ago

Note that you are given a degree 10 polynomial. Review Vieta's Formula

Calvin Lin Staff - 6 years, 9 months ago

what is vieta's theorem

Sourav Paul - 6 years, 7 months ago

Overrated!

Kartik Sharma - 6 years, 9 months ago

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Krishna Ar - 6 years, 9 months ago

me to
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Parth Lohomi - 6 years, 9 months ago

@Parth Lohomi – Parth, is that your expression to Kartik's reaction or my reaction to Kartik's reaction?

Krishna Ar - 6 years, 9 months ago

@Krishna Ar – That's my reaction to your reaction to kartik's reaction!

Parth Lohomi - 6 years, 2 months ago

William Isoroku
Sep 16, 2014

We know that the sum of the roots is (-b/c) where b is the coefficient is the second highest power in descending order, which is x^9. Therefore the sum is 0 since there is x^9. So substitute X=0 into the last equation to obtain 7.

a very simple equation

The answer is 7.

2 solutions

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