Roots of a 4th degree polynomial

  1. 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)
     
    Last edited: Nov 12, 2006
  2. jcsd
  3. Pyrrhus

    Pyrrhus 2,273
    Homework Helper

    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.
     
  4. Hurkyl

    Hurkyl 16,089
    Staff Emeritus
    Science Advisor
    Gold Member

    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.


    Is there any reason why you can't simply define r to be a root of that polynomial, and then work with r?
     
    Last edited: Nov 12, 2006
  5. 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.
     
  6. Pyrrhus

    Pyrrhus 2,273
    Homework Helper

  7. 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 :)
     
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