ts547 said:Homework Statement
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
Homework Equations
Finding this very complicated to solve, are there any useful hints or techniques we should know about?
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.
You can see the LaTeX I wrote by clicking the equation.ts547 said:Yeh that's it. I haven't learned how to do the fancy writing yet. I didnt think there would be an easy way of doing this.
A polynomial is an algebraic expression that consists of variables and coefficients, combined using addition, subtraction, and multiplication, but never division, exponents, or radicals.
Some common techniques for solving polynomials include factoring, using the quadratic formula, and using long division or synthetic division. Other methods include graphing and using the rational roots theorem.
A polynomial has solutions if and only if it has at least one real root, which is a value for the variable that makes the polynomial equal to zero. This can be determined by graphing the polynomial or by using the rational roots theorem.
No, not all polynomials can be solved using the same techniques. The methods used to solve a polynomial depend on its degree (the highest exponent) and its form. For example, a polynomial with a degree of 2 (quadratic) can be solved using the quadratic formula, while a polynomial with a degree of 3 (cubic) can be solved using the cubic formula.
One tip for solving polynomials more efficiently is to always start by factoring, if possible. This can help simplify the polynomial and make it easier to solve. Another tip is to look for patterns or common factors in the polynomial, as this can also make solving it easier.