The abscissas of the 
-point Gaussian quadrature formula are precisely the roots
of the orthogonal polynomial for the same
interval and weighting
function.
Fundamental Theorem of Gaussian Quadrature
See also
Gaussian QuadratureExplore with Wolfram|Alpha
Cite this as:
Weisstein, Eric W. "Fundamental Theorem of Gaussian Quadrature." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/FundamentalTheoremofGaussianQuadrature.html