Problem #PRU-61136

Problems Methods Examples and counterexamples. Constructive proofs Pigeonhole principle Pigeonhole principle (other) Set theory and logic Theory of algotithms Theory of algorithms (other)

Problem

Let f(x) be a polynomial of degree n with roots α1,,αn. We define the polygon M as the convex hull of the points α1,,αn on the complex plane. Prove that the roots of the derivative of this polynomial lie inside the polygon M.