MathDB

Prove that 2p(-1) is a multiple of p(1)+p(-1)-2(1+p(0))

Source: IMO LongList 1982 - P15

September 10, 2010

algebrapolynomialrootsCubicIMO ShortlistIMO Longlist

Problem Statement

Let

p(x)

be a cubic polynomial with integer coefficients with leading coefficient

1

and with one of its roots equal to the product of the other two. Show that

2p(-1)

is a multiple of

p(1)+p(-1)-2(1+p(0)).