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Polynomial roots or discriminant

  1. Jul 24, 2013 #1
    Hi there,

    I was wondering if it is possible to find the roots of the following polynomial
    [tex]
    P(x)=x^n+a x^m+b
    [/tex]
    or at least can I get the discriminant of it, which is the determinant of the Sylvester matrix associated to P(x) and P'(x).

    Thanks
     
  2. jcsd
  3. Jul 24, 2013 #2

    micromass

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    The Abel-Ruffini theorem says that it's impossible to find the roots of ##x^5 - x +1## using only rational numbers and radicals and combinations of those. So that's a counterexample to being able to find all the roots.
     
  4. Jul 24, 2013 #3
    Yes that's true, then do you have any idea how to get the discriminant ?
     
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