MathDB
p(x)+ p'(x)+ p''(x)+...+ p^{(n)}(x) >= 0 if p(x) >= 0

Source: 1985 Swedish Mathematical Competition p4

March 28, 2021
analysisalgebrapolynomial

Problem Statement

Let p(x)p(x) be a polynomial of degree nn with real coefficients such that p(x)≥0p(x) \ge 0 for all xx. Prove that p(x)+p′(x)+p′′(x)+...+p(n)(x)≥0p(x)+ p'(x)+ p''(x)+...+ p^{(n)}(x) \ge 0.
Back to ProblemsView on AoPS