P15.2.2 The Legendre polynomials satisfy Lo(z) = 1, Li (z) = z, LN+1(x) = 2 z4x(z)-4x-1 (z) for N > 1. b) Determine the zero of L close to 0.5 using Newton's method. c) Determine all roots of L4 by computing the eigenvalues of a symmetric matrix