## Solving polynomials

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

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

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## Solving polynomials

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.

Mentor
 Quote by 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.
You can see the LaTeX I wrote by clicking the equation.
 Heck, I managed to simplify it this equation (check work?): $$(\frac{15}{x^3} - \frac{6}{x})sin(x) + (1 - \frac{15}{x^2})cos(x) = \frac{1}{6}$$ Edit: LaTeX isn't the easiest, heh. Also, I'm not sure that simplification is even very useful.
 Recognitions: Gold Member Science Advisor Staff Emeritus I hope that you are aware that this is not a matter of "solving polynomials"! The equation you give is not a polynomial.
 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.

 Tags minimizing, polynomials, solving