### Roots of a Polynomial

Posted:

**Tue Jan 09, 2018 10:17 am**Is there a general expression to find the roots of the following polynomial?

$z^n + n z^{n - 1} + n(n - 1)z^{n - 2} + n(n - 1)(n - 2)z^{n - 3} + \cdots + n! = 0$?

The structure of the polynomial seems to suggest there can be something that can be done to evaluate the roots explicitly but I can't see it. Any help? Thanks.

$z^n + n z^{n - 1} + n(n - 1)z^{n - 2} + n(n - 1)(n - 2)z^{n - 3} + \cdots + n! = 0$?

The structure of the polynomial seems to suggest there can be something that can be done to evaluate the roots explicitly but I can't see it. Any help? Thanks.