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Math Help - Proving inequality

  1. #1
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    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
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  2. #2
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    Quote Originally Posted by maria18 View Post
    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.
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