Solving polynomials

ts547

1. The problem statement, all variables and given/known data

Solve for x,

225*sin(x)/x^6-225*cos(x)/x^5-90*sin(x)/x^4+15*cos(x)/x^3-5/(2*x^3)=0


2. Relevant equations

Finding this very complicated to solve, are there any useful hints or techniques we should know about?


3. The attempt at a solution

Have used numerical method using mathematics software and plotted a graph to identify where the function crosses the x-axis. Would prefer a more analytic approach.

Thank you in advance.

Mark44

I think that you are out of luck regarding an analytic solution.

BTW, is this your equation?
[tex]225\frac{sin(x)}{x^6} - 225 \frac{cos(x)}{x^5} - 90\frac{sin(x)}{x^4} + 15\frac{cos(x)}{x^3} - \frac{5}{2x^3} = 0[/tex]

ts547

Yeh thats it. I havent learnt how to do the fancy writing yet. I didnt think there would be an easy way of doing this.

gb7nash

Unless there's some funny trick to recognize here, there's no way to solve this algebraically. It's best to use a numerical technique. i.e. Bisection method, Newton's method, etc.

Mark44

You can see the LaTeX I wrote by clicking the equation.

Apphysicist

Heck, I managed to simplify it this equation (check work?):

[tex]
(\frac{15}{x^3} - \frac{6}{x})sin(x) + (1 - \frac{15}{x^2})cos(x) = \frac{1}{6}
[/tex]

Edit: LaTeX isn't the easiest, heh. Also, I'm not sure that simplification is even very useful.

HallsofIvy

I hope that you are aware that this is not a matter of "solving polynomials"! The equation you give is not a polynomial.

ts547

Apphysicist - Haha good simplification. Not very useful I dont think. :) Never mind ill stick with the numerical approach.

HallsofIvy - Ok no its not a polynomial. Didnt know what else to call it at the time. If your so clever help me with this

http://www.physicsforums.com/showthr...32#post3075732

then you can point out technicalities all you want.