I know there's no general formula for all the roots of a polynomial with a degree greater than 4, but is there some sort of limit (or other) definition to calculate the roots (particularly the largest root)?



Is there a limit definition for the roots of a polynomial with arbitrary degree?
For computing the largest root, see the [Graeffe Method.](https://www.wikiwand.com/en/Graeffe's_method)


For bounding the largest root, there are many bounds, see [the Wikipedia article](https://www.wikiwand.com/en/Properties_of_polynomial_roots) (which is incomplete, but since you don't tell us what you want, maybe that's good enough).


