Let f(x) 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 α∈[0,1], there exists a \zeta \in [\minus{}1,\plus{}1] such that |f'(\zeta)|\equal{}\alpha and that this statement is not true if α>1. algebrapolynomialalgebra proposed