9 = -1 2 and let P(z) = do + 012+ + adza, ad + 0 be a polynomial with real coefficients such that lajl s 1 for j = 0),1,...,d. The purpose of this exercise is to show the existence of a polynomial f(z) = co + Cl2 + ... + Cazd, where c; = +1 for j = 0,1,...,d and f well approximates P, i.e., max |P(z) - f(3) = 0 {\dlogd), by employing the probabilistic method based on the next steps. (a) Show that P satisfies |P(z) P(w)|