Solve without a calculator – 6

Algebra Level pending

Find the product 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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1 solution

Parth Sankhe
Nov 17, 2018

Product of all roots = ±constant term÷ x n x^n coefficient

No constant term, hence product=0

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Shenghui Lin - 2 years, 6 months ago

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