# Roots of a 4th degree polynomial

by Grantismo
Tags: degree, polynomial, roots
 P: 4 Hi eveveryone I was just hoping for some quick help on frustrating physics related math problem. I won't go into detail on the actual problem becasue i know i found the correct polynomial but i was wondering if there was any easy way to find the roots to this polynomial: 3x^4-960x^3+91500x^2-6272000x+501760000=f(x) *sorry i haven't figured out how to use latex or w/e it's called* rational roots seems rather arduous with the numbers involved. Any suggestions?(I know there is only one answer about 125.98 i think but i was wondering if there was a way to find an exact answer algebraically or with calculus or something)
 HW Helper P: 2,277 Apart from using Ruffini's method (rational roots) or Newton's method, both which will require time to yield answers, maybe since this isn't a mathematical problem you can use Mathematica, Matlab, etc... for your solutions. Also you could have tried Descartes' sign rule, but that wouldn't have helped much anyway.
Emeritus
PF Gold
P: 16,091
 rational roots seems rather arduous with the numbers involved.
501760000 isn't a very big number. A computer should be able to factor that before you can blink. It can probably plug every number dividing 501760000 into that polynomial roughly as quickly.

 i was wondering if there was a way to find an exact answer algebraically
Is there any reason why you can't simply define r to be a root of that polynomial, and then work with r?

 P: 4 Roots of a 4th degree polynomial I don't think that the roots are rational now that i've looked at a it or a while, Cyclovenom if you could explain any of those methods i might try them.
HW Helper
P: 2,277
 Quote by Grantismo I don't think that the roots are rational now that i've looked at a it or a while, Cyclovenom if you could explain any of those methods i might try them.
Certainly, i will try to answer any questions about the methods, but they are explained in these sites:

Newton's Method