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Math Help - Quadratic Question

  1. #1
    Senior Member Stroodle's Avatar
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    Quadratic Question

    Hi,

    This is probably a relatively easy question, but I've never done this before, and I'm not sure how to go about it.

    For the equation 3x^2+ax+4=0 find the smallest possible value of a such that the equation will have two distinct rational solutions.

    Thanks for your help

    *Edit - Never-mind. I just figured it out
    Last edited by Stroodle; July 23rd 2009 at 03:19 AM.
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  2. #2
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    So please mark this thread [SOLVED]
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  3. #3
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    Hello, Stroodle!

    For the equation 3x^2+ax+4\:=\:0, find the smallest possible value of a
    such that the equation will have two distinct rational solutions.

    Thanks for your help

    *Edit - Never-mind. I just figured it out
    Good for you!


    But is this a trick question?
    I noted that it didn't say smallest positive value of a.

    Using the Quadratic Formula: . x \;=\;\frac{-a \pm\sqrt{a^2-48}}{6}

    For rational roots, the discriminant (a^2-48) must be a square.

    This is true for: . a \;=\;\pm7,\:\pm8,\:\pm13

    Then the smallest (least) value of a is: . a \:=\:-13

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  4. #4
    Senior Member Stroodle's Avatar
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    Haha. Well spotted Soroban!

    Actually the question did ask for the smallest positive value of a, but in my tired & vague state of mind I accidentally failed to copy it down...
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