Problem #PRU-61136

Problems Methods Examples and counterexamples Pigeonhole principle Pigeonhole principle (other) Set theory and logic Algorithm Theory Algorithm Theory

Problem

Let \(f (x)\) be a polynomial of degree \(n\) with roots \(\alpha_1, \dots , \alpha_n\). We define the polygon \(M\) as the convex hull of the points \(\alpha_1, \dots , \alpha_n\) on the complex plane. Prove that the roots of the derivative of this polynomial lie inside the polygon \(M\).