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Math Help - Can anyone solve this cubic for me?

  1. #1
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    Can anyone solve this cubic for me?

    24x^3+24x^2-36x+18=0

    Anyone? Thanks!
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  2. #2
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    Last edited by mr fantastic; February 8th 2010 at 01:56 AM. Reason: Added url link tags.
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  3. #3
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    Quote Originally Posted by BigMath View Post
    24x^3+24x^2-36x+18=0

    Anyone? Thanks!
    The first thing I would do is divide the equation by 6:
    4x^2+ 4x^2- 6x+ 3= 0

    Then I would use the "rational root theorem": any rational roots of this equation must be a fraction with numerator a factor of 3 and denominator a factor of 4. That is, the numerator must be one of \pm 3, or \pm 1 and the denominator must be one of \pm 4, \pm 2, or \pm 1. There are 12 possible combinations. Try each of those. If you find a rational root among those, then you can reduce the equation to a quadratic to find the other roots.

    If there is no rational root, then you will just have to use Cardano's formula, which is terribly messy.
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