Answer to Question #104404 in Algebra for Sourav Mondal

Question

Find the value of a for which the polynomial x^5-ax²-ax+1has −1 as a root with multiplicity at least 2.

Answer 1

it is possible if a = -5. Indeed, x⁵-ax²-ax+1=(x+1)(x⁴-x³+x²-x+1)-ax(x+1)=(x+1)(x⁴-x³+x²-x+1-ax)=(x+1)(x+1)(x³-2x²+3x+1)