Miklos Schweitzer 1949_5
Source:
October 2, 2008
algebrapolynomialalgebra proposed
Problem Statement
Let be a polynomial of second degree the roots of which are contained in the interval [\minus{}1,\plus{}1] and let there be a point x_0\in [\minus{}1.\plus{}1] such that |f(x_0)|\equal{}1. Prove that for every , there exists a \zeta \in [\minus{}1,\plus{}1] such that |f'(\zeta)|\equal{}\alpha and that this statement is not true if .