Polynomial roots or discriminant

[nergal]

Hi there,

I was wondering if it is possible to find the roots of the following polynomial
$$P(x)=x^n+a x^m+b$$
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

 

[micromass]

Hi there,

I was wondering if it is possible to find the roots of the following polynomial
$$P(x)=x^n+a x^m+b$$

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.

 

[nergal]

Yes that's true, then do you have any idea how to get the discriminant ?