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Math Help - Determine all values of k

  1. #1
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    Determine all values of k

    Determine all values of k so that the trinonmial can be factored using integers

    c^2+kc-24

    I think it might be 10 and 2 but im really not so sure. :/

    Help please
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  2. #2
    Super Member Bacterius's Avatar
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    Quote Originally Posted by HAGEMONSTER View Post
    Determine all values of k so that the trinonmial can be factored using integers

    c^2+kc-24

    I think it might be 10 and 2 but im really not so sure. :/

    Help please
    Do you know the discriminant ? If yes, then you know that if the discriminant is a perfect square, the quadratic can be factored over the integers. Here the discriminant is equal to :

    \Delta = k^2 + 96

    So, it means that for some a^2, the following holds :

    a^2 = k^2 + 96

    Or, rearranging :

    a^2 - k^2 = 96

    Finally :

    (a - k)(a + k) = 96

    Now you can factorize 96 and see which values of k actually satisfy this equation. I'm pretty sure you are right with 2 and 10.
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  3. #3
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    thanks so mu8ch
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