Solve without a calculator – 5

Algebra Level 2

Find the sum of all (complex) roots of the polynomial

f ( x ) = 1 7 x 7 − 534 7 x 5 + 11487 x 3 − 396508 x f(x) = \frac 17 x^7 - \frac {534}7 x^5 + 11487 x^3 -396508x


The answer is 0.

Henry U by Henry U , 17, Germany

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2 solutions

Chew-Seong Cheong
Nov 18, 2018

Relevant wiki: Vieta's Formula - Higher Degrees

By Vieta's formula, we have the sum of all roots is the coefficient of x 6 x^6 in the equation which is 0 \boxed 0 .

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Parth Sankhe
Nov 17, 2018

Sum of roots of an n n degree equation = - coefficient of x ( n − 1 ) x^{(n-1)} ÷ coefficient of x n x^n

There is no x 6 x^6 term, therefore answer is 0.

1 Helpful 0 Interesting 0 Brilliant 0 Confused

That sounds very interesting! I didn't know of it.

Henry U - 2 years, 6 months ago

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