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Math Help - Quadratic Inequality

  1. #1
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    Exclamation Quadratic Inequality

    Find the range of values of k if kx^2 + 8x > 6 - k for all real values of x.

    The answer given is k > 8.
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  2. #2
    Senior Member Sambit's Avatar
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    Find its discriminant and solve the equation discriminant=0 for k; then take a value of k which (i) is smaller than the smaller root, (ii) is higher than the higher root and (iii) lies between the two roots. Take that region which satisfies the equation you mentioned.
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  3. #3
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    I am getting the answer as k > -2 or k > 8. Why is only k > 8 specified in the answer?
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  4. #4
    MHF Contributor

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    You have two errors: you get x> 2 (not -2) and x> 8 (not or). In order that both of those be true, x must be greater than 8.
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