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Thread: inequality

  1. #1
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    inequality

    Hello!
    Please help me to solve this inequality!
    p(x^2+2)<2x^2+6x+1, if p is parameter!
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  2. #2
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    You want to solve for $\displaystyle x$?
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  3. #3
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    yes!
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  4. #4
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    Do you know the quadratic formula?

    When you have $\displaystyle ax^2+bx+c=0,x=\frac{-b\pm\sqrt{b^2-4ac}}{2a} $

    In your case.

    $\displaystyle p(x^2+2)<2x^2+6x+1$

    $\displaystyle px^2+2p<2x^2+6x+1$

    $\displaystyle 0<2x^2-px^2+6x+1-2p$

    $\displaystyle 2x^2-px^2+6x+1-2p<0$

    $\displaystyle (2-p)x^2+6x+1-2p<0$

    Now use $\displaystyle a = 2-p, b=6, c = 1-2p$ into the quadratic formula
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