This should be done with Python

And here are Newton's method and roots of eigenvalues.

P15.2.2 The Legendre polynomials satisfy 1, L1(2)=x, LN41( NT LN)LN-1(x) for N 2 1 b) Determine the zero of L4 close to 0.5 using Newton's method. c) Determine al roots of Ls by computing the eigenvalues of a symmetric matrix. P15.2.2 The Legendre polynomials satisfy 1, L1(2)=x, LN41( NT LN)LN-1(x) for N 2 1 b) Determine the zero of L4 close to 0.5 using Newton's method. c) Determine al roots of Ls by computing the eigenvalues of a symmetric matrix