If $P(x)$ is a polynomial of degree $5$ and $$\alpha=\sum_{i=0}^6P(x_i)\bigg(\prod_{j=0, j\neq i}^6(x_i-x_j)^{-1}\bigg),$$ where $x_0, x_1, \ldots , x_6$ are distinct points in the interval $[2, 3]$, then show that $\alpha^2 -\alpha =0$.
I am not able to start this problem. Any hint is appreciated.