MathDB

7

Part of 1982 IMO Shortlist

Problems(1)

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

Source: IMO LongList 1982 - P15

9/10/2010
Let p(x)p(x) be a cubic polynomial with integer coefficients with leading coefficient 11 and with one of its roots equal to the product of the other two. Show that 2p(−1)2p(-1) is a multiple of p(1)+p(−1)−2(1+p(0)).p(1)+p(-1)-2(1+p(0)).
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