hi, need help thanks

Let be $\displaystyle a,b,c\in \mathbb{R}$ such that $\displaystyle |ax^2 + bx + c|\le 1\ ,\ (\forall)x\in [ - 1,1]$ . If $\displaystyle \alpha \in [0,1] $show that :

$\displaystyle \alpha(1 + \alpha)|b| + (10 - \alpha^2)|c|\le 1 + \alpha^2$