Please solve this numerical analysis problem.

21. (4.7-13/7) Verify the entries of the Roots and the Coefficients of the Gaussian quadrature rules shown below, for the values of n = 2 and 3, by finding the roots of the respective Legendre polynomials, and use the equations in the Theorem to find the coefficients associated with the values. n Roots rn,i Coefficients Cn,i 2 0.5773502692 1.0000000000 -0.5773502692 1.0000000000 3 0.7745966692 0.5555555556 0.0000000000 0.8888888889 -0.7745966692 0.5555555556