  We derive explicit formulas for the resultants and discriminants of classical
quasi-orthogonal polynomials, as a full generalization of the results of
Dilcher and Stolarsky (2005) and Gishe and Ismail (2008). We consider a certain
system of Diophantine equations, originally designed by Hausdorff (1909) as a
simplification of Hilbert's solution (1909) of Waring's problem, and then
create the relationship to quadrature formulas and quasi-Hermite polynomials.
We reduce these equations to the existence problem of rational points on a
hyperelliptic curve associated with discriminants of quasi-Hermite polynomials,
and thereby show a nonexistence theorem for solutions of Hausdorff-type
equations.
