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.
Re: Non Numeric roots of a polynomial
not every root of a polynomial is of the form . 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.