$$Q_{\alpha}(f) = \lambda_{(\alpha,1)} f(0) + \lambda_{(\alpha,2)} f(\alpha) +\lambda_{(\alpha,3)} f(1)$$
$$\alpha \in (0,1) $$
$$ f:[0,1] \rightarrow \mathbb{R}$$
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?

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?