From Wolfram MathWorld:
The fundamental theorem of Gaussian quadrature states that the optimal abscissas of the m-point Gaussian quadrature formulas are precisely the roots of the orthogonal polynomial for the same interval and weighting function.
In this context, what is meant by "the orthogonal polynomial"? To be orthogonal is not a property of any particular polynomial, but rather a set of polynomials. Thanks all!