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Roots of a 4th degree polynomial

by Grantismo
Tags: degree, polynomial, roots
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Grantismo
#1
Nov12-06, 10:00 PM
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)
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Pyrrhus
#2
Nov12-06, 10:33 PM
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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
#3
Nov12-06, 10:45 PM
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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
#4
Nov12-06, 11:18 PM
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.
Pyrrhus
#5
Nov12-06, 11:57 PM
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Quote 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

http://www.ugrad.math.ubc.ca/coursed...ox/newton.html

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

Ruffini's Method

http://en.wikipedia.org/wiki/Ruffini's_rule
Grantismo
#6
Nov13-06, 12:08 AM
P: 4
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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