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two quadratic polynomials

Source: Russian 2007

August 25, 2007
quadraticsalgebrapolynomialalgebra proposedPolynomials

Problem Statement

Two quadratic polynomials f1,f2 f_{1},f_{2} satisfy f_{1}'(x)f_{2}'(x)\geq |f_{1}(x)|\plus{}|f_{2}(x)|\forall x\in\mathbb{R} . Prove that f_{1}\cdot f_{2}\equal{} g^{2} for some g∈R[x] g\in\mathbb{R}[x].
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