Two-node Gaussian quadrature with linear weight
= Two-node Gaussian quadrature with linear weight
{title2=$x_{1,2}=(6\mp\sqrt6)/10$}
For weight $w(x)=x$ on $[0,1]$, the two-node <Gaussian quadrature> nodes are roots of $x^2-6x/5+3/10$, the monic quadratic orthogonal to all linear <polynomials>. Its weights come from integrating the <Lagrange interpolation> cardinal functions. Orthogonality gives exactness on cubic <polynomials> and positive weights.