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Polynomial divisible by x^2+1

Source: Tuymaada 2018 Junior League/Problem 1

July 20, 2018
algebrapolynomial

Problem Statement

Real numbers a≠0,b,ca \neq 0, b, c are given. Prove that there is a polynomial P(x)P(x) with real coefficients such that the polynomial x2+1x^2+1 divides the polynomial aP(x)2+bP(x)+caP(x)^2+bP(x)+c.
Proposed by A. Golovanov
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