Problem #PRU-111763

Problems Calculus Derivative Calculating a derivative Algebra Absolute value Inequalities containing absolute values Polynomials Quadratic polynomials Quadratic polynomilal (other)

Problem

The quadratic trinomials \(f (x)\) and \(g (x)\) are such that \(f' (x) g' (x) \geq | f (x) | + | g (x) |\) for all real \(x\). Prove that the product \(f (x) g (x)\) is equal to the square of some trinomial.