Roots of a 4th degree polynomial

[Grantismo]

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)

 

[Pyrrhus]

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.

 

[Hurkyl]

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?

 

[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.

 

[Pyrrhus]

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

http://www.ugrad.math.ubc.ca/coursedoc/math100/notes/approx/Newton.html"

http://www.sosmath.com/calculus/diff/der07/der07.html"

Ruffini's Method

"[URL

 

[Grantismo]

wow, the Newton method is PERFECT for what I wanted, plus it will also give my teacher a huge laugh (inside joke about approximations)
Thank you SOO much :)