How to solve an nth degree polynomial equation The typical approach of solving a quadratic equation is to solve for the roots
$$x=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}$$
Here, the degree of x is given to be 2
However, I was wondering on how to solve an equation if the degree of x is given to be n.
For example, consider this equation:
$$a_0 x^{n} + a_1 x^{n-1} + \dots + a_n = 0$$

An approach that immediately comes to mind is to first establish the relationship (non-linear, typically) between each root of the polynomial (assumed, complex) and the coefficients of the power series, and then solve the resulting set of $n$ equations for the $n$ variables i.e, the roots, using an iterative numerical algorithm (say, Newton-Raphson extended to $n$ equations in $n$ variables) computed in the complex domain (to ensure convergence).
A pretty good approach to get the power series coefficients is by using discrete convolution for polynomial multiplication (see here ).  

However, I was wondering on how to solve an equation if the degree of $x$ is given to be $n$.  

The only thing that's now between you and your solutions (all $n$ of them) is a computer program.
