How do i find the roots of this polynomial?

[iScience]

x^3-5x-6=0

i've tried the p/q calculations in accordance with the rational roots theorem but I've yet to find the answers...

 

[SteamKing]

You can either:
1. Use trial and error to find a solution.
2. Graph the equation in order to estimate a solution.
3. Use the formula for the roots of a cubic equation (most complicated approach).

See: http://en.wikipedia.org/wiki/Cubic_function

 

[D H]

4. Use an approximation scheme such as regula falsi, secant method, or Newton's method.

The rational root theorem says yields a small number of candidate rational roots. Not a single one of those candidates will yield a root. That doesn't mean there aren't any roots. It just means the root/roots aren't rational numbers.