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Math Help - values of k

  1. #1
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    values of k

    hi, i'm stuck on a question and would like some help please:

    find the values for k for which the quadratic equation 3x^2 + (6 - k)x + 12 = 0 has equal roots. i used the discriminant theory and got it to \sqrt{36 - 12k + k^2 - 144} = \sqrt{-108 - 12k + k^2} and then - 12k + k^2 = 108 but i'm really not sure if any of this is right. could someone show me if this is the right way?

    thanks, Mark
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  2. #2
    MHF Contributor red_dog's Avatar
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    You have to solve the quadratic k^2-12k-108=0 and find k.
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  3. #3
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    i see, where did the 8 come from?
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  4. #4
    MHF Contributor red_dog's Avatar
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    Sorry, it's 0 not 8. I pushed the wrong button. I edited.
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  5. #5
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    Talking

    Quote Originally Posted by mark View Post
    find the values for k for which the quadratic equation 3x^2 + (6 - k)x + 12 = 0 has equal roots.
    For the roots to be equal, the "plus minus" part must be zero. This means that:

    . . . . . (6\, -\, k)^2\, -\, 4(3)(12)\, =\, 0

    . . . . . 36\, -\, 12k\, +\, k^2\, -\, 144\, =\, 0

    . . . . . k^2\, -\, 12k\, -\, 108\, =\, 0

    That's where the earlier helper got his/her equation.

    Now apply the Quadratic Formula to this equation to find the value(s) of k.
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