Problem

Source: RMO 2017 P3

Tags: algebra, Real Roots



Let \(P(x)=x^2+\dfrac x 2 +b\) and \(Q(x)=x^2+cx+d\) be two polynomials with real coefficients such that \(P(x)Q(x)=Q(P(x))\) for all real \(x\). Find all real roots of \(P(Q(x))=0\).