# Proving inequality

• Apr 15th 2009, 02:44 PM
maria18
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 :

$\alpha(1 + \alpha)|b| + (10 - \alpha^2)|c|\le 1 + \alpha^2$
• Apr 16th 2009, 08:03 AM
Opalg
Quote:

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.