I want to construct a gauss integration for the weight function $w(x) = x^{1/2}$ for
$$\int_{0}^{1}x^{1/2}f(x)dx = a_{1}f(x_{1})+a_{2}f(x_{2})$$
Solving
\begin{align*} a_{1}+a_{2} =& \int_{0}^{1}x^{1/2} dx = \frac{2}{3} \\ a_{1}x_{1}+a_{2}x_{2}=&\int_{0}^{1}x^{1/2}x dx =\frac{2}{5}\\ \end{align*}
Solving this system will yield $ a_{1},a_{2}$? and then what?