# Math Help - Proving inequality

1. ## Proving inequality

hi, need help thanks

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

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

2. Originally Posted by maria18
hi, need help thanks

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

$\alpha(1 + \alpha)|b| + (10 - \alpha^2)|c|\le 1 + \alpha^2$
You need to make sure that you have posted the problem correctly. As stated, this result cannot be true. For example, when $\alpha=0$ it says that $10|c|\leqslant1$, which certainly need not be true.