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)
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.
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?
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 http://en.wikipedia.org/wiki/Ruffini's_rule
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 :)