Using the result of Theorem 64 find the weights and the node

Using the result of Theorem 6.4, find the weights and the nodes of the two- and three-point Gauss-Legendre quadrature formulas. Find the weights by undetermined second- and third-degree monic Legendre polynomials are respectively The weights can be verified by checking precision in (6.34).]

Solution

mention theorem 6.4 also