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p(x)\geq0 [Similiar to Shortlist]

Source: Iranian National Olympiad (3rd Round) 2006

September 19, 2006

algebrapolynomialalgebra proposed

Problem Statement

p(x)

is a real polynomial that for each

x\geq 0

p(x)\geq 0

. Prove that there are real polynomials

A(x),B(x)

that

p(x)=A(x)^{2}+xB(x)^{2}