Problem - 2594
Let $\alpha$ and $\beta$ be the two roots of $x^2 + 2x -5=0$. Evaluate $\alpha^2 + \alpha\beta + 2\alpha$.
By Vieta's theorem, we have
$$\alpha^2 + \alpha\beta + 2\alpha = \alpha(\alpha + \beta) + 2\alpha=-2\alpha+2\alpha=\boxed{0}$$