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Math Help - Non Numeric roots of a polynomial

  1. #1
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    Non Numeric roots of a polynomial

    I want to calculate non numeric roots of a polynomial in the form a+sqr(b)/c. For example numeric roots of the polynomial f(x)=x4-270x2-140x+1200 are
    Root 1: -16.018
    Root 2: -2.413
    Root 3: 1.876
    Root 4: 16.555
    But i want to calculate in the form a+sqr(b)/c. Actually i am interested in discriminant b. is there any program which calculate roots in a+sqr(b)/c form.
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  2. #2
    MHF Contributor

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    Tejas
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    Re: Non Numeric roots of a polynomial

    not every root of a polynomial is of the form \frac{a+\sqrt{b}}{c}. while something akin to the discriminant for the quadratic exists for cubic equations, and quartics can be solved in terms of their resolvent cubics, for polynomials of degree > 4, there is no general formula at all.

    wolframalpha.com and its "parent" program mathematica (and maple, too, i suspect, i don't have experience with that program much) will display roots in an exact form, if there is one. be prepared for some very ugly formulas.
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