MathDB
Polynomials

Source: Iranian National Olympiad (3rd Round) 2006

September 19, 2006
algebrapolynomialfunctioncomplex analysisdomainalgebra proposed

Problem Statement

P,Q,RP,Q,R are non-zero polynomials that for each z∈Cz\in\mathbb C, P(z)Q(zˉ)=R(z)P(z)Q(\bar z)=R(z). a) If P,Q,R∈R[x]P,Q,R\in\mathbb R[x], prove that QQ is constant polynomial. b) Is the above statement correct for P,Q,R∈C[x]P,Q,R\in\mathbb C[x]?
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