MathDB

11.2

Part of 2007 All-Russian Olympiad Regional Round

Problems(1)

two quadratic polynomials

Source: Russian 2007

8/25/2007
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].
quadraticsalgebrapolynomialalgebra proposedPolynomials