Question

\[Q_{\alpha}(f) = \lambda_{(\alpha,1)} f(0) + \lambda_{(\alpha,2)} f(\alpha) +\lambda_{(\alpha,3)} f(1)\]
\[\alpha \in (0,1) \]
\[ f:[0,1] \rightarrow \mathbb{R}\]
a) Solve the weights \[\lambda_{\alpha,i} \]in dependency to \[\alpha\]so that the quadrature formula \[Q_\alpha\]is exact for every polynome of degree 2.
b) For which \[\alpha \in (0,1)\]is the quadrature formula positive?