General formula for special Polynomial

is there a special formula to find the roots of a polynomial like

$$P(x) = x^{b+c} + \alpha x^b + \beta x^c -\gamma = 0$$

• b,c are natural numbers? – Loreno Heer Oct 27 '15 at 18:08
• I guess it is relevant for your purposes to notice that $P(x)=0$ is equivalent to $(x^b+\beta)(x^c+\alpha)=(\gamma-\alpha\beta).$ – Jack D'Aurizio Oct 27 '15 at 18:08
• Yes, b and c are natural – user284463 Oct 27 '15 at 18:13

$$P(x) = (x^{b}+\beta)(x^c+\alpha)+(\alpha \beta - \gamma)$$
so the roots are easy to find in the case that $\alpha \beta - \gamma=0$