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Math Help - finding roots of cubics and quartics

  1. #1
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    Arrow finding roots of cubics and quartics

    How can I find the roots of these equations. I.E, how can I factor the cubic to get a binomial and a quadratic so then I can use the quad. formula for the last two factors?

    TYIA

    10x^3-x^2+5x+4=0

    also

    3x^4+2x^3+7x^2+8x-20=0
    Last edited by hello; September 27th 2009 at 02:19 PM.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by hello View Post
    How can I find the roots of these equations. I.E, how can I factor the cubic to get a binomial and a quadratic so then I can use the quad. formula for the last two factors?

    TYIA

    10x^3-x^2+5x+4=0

    also

    3x^4+2x^3+7x^2+8x-20=0
    You can use the rational roots theorem to give a list of candidate rational roots which you then check to see if one or more is an actual root.

    The rational root theorem says that any rational root of a polynomial equation is the ratio of a factor of the constant terma and the coeficient of the highest order term.

    so for the cubic here the list of candidates is:

    \pm 1,\ \pm 2,\ \pm4,\ \pm1/2,\ \pm 1/5,\ \pm 2/5,\ \pm 4/5,\ \pm 1/10

    CB
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