Question 5 (12 Marks) Let P be differentiable on R, one version of Rolle's theorem states "between the zeros of F there is a zero of F. a) Verify this theorem for the polynomials Fi = (x-1)(z-2) F2 = (z-1)(z-2)(z-3), by finding the zeros of both F and F. b) Now suppose that F is differentiable on R. Write down a one line statement in which Rolle's theorem is applied to F', and verify your new theorem for F2. c) Let G = x" +ax + b, where n is a positive integer and a and b are non-zero real constants. Make use of part (a) to prove that: (i) if n is even then G has at most two zeros, (ii) if n is odd then G has at most three zeros