3. Let d 2 and let P(z) = a + az + ... + adz, ad 0 be a polynomial with real coefficients such that laj1 for j = 0,1,..., d. The purpose of this exercise is to show the existence of a polynomial f(z) = co+c12+. ... + caz, where c; = 1 for j = 0,1,...,d and f well approximates P, i.e., max |P(z) = f(z)| = O(d log d), by employing the probabilistic method based on the next steps. (a) Show that P satisfies |P(z) - P(w)| d|zw| for all z, w [1,1]. Hint; you may show that |P'(z)|