finding the roots of polynomial of degree 5

Question

I want to find the roots of $f(x)=x^5+(2-4n)x^4-10nx^3+(24n^2-16n-2)x^2+(20n^2-6n-1)x-16n^3+4n^2+4n$ with maple, but with

solve(f=0,x);

it give me

RootOf(_z^5+(2-4n)_z^4-10nx^3+(24n^2-16n-2)_z^2+(20n^2-6n-1)_z-16n^3+4n^2+4n)

is there any mathematical software to give me the exact roots of $f(x)$?

There is no techniques for solving polynomials with degree higher than four in general. — science, Mar 01 '15 at 06:22
This is false. There is an algorithm for finding the roots of any polynomial with rational coefficients. — William Stagner, Mar 01 '15 at 06:57

score 1 · Answer 1 · edited Apr 13 '17 at 12:21

1

There is no general formula for the exact roots involving only radicals. In this question they explain how to do it with elliptic functions: How to solve fifth-degree equations by elliptic functions?

I don't know of any software that does this automatically.

edited Apr 13 '17 at 12:21

Community

1

answered Mar 01 '15 at 06:57

Matt Samuel

58,164

score 0 · Answer 2 · answered Mar 01 '15 at 06:58

0

Did you try Ruffini rule? Write it on a table and try n as a parameter. The residual has to be a function in variable n which you have to make equal zero.

answered Mar 01 '15 at 06:58

Alberto

1

may you give me more explain? How can I find the first root? – M.Mehranian Mar 01 '15 at 14:13

finding the roots of polynomial of degree 5

2 Answers2