General formula for special Polynomial

Question

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

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

Answer 1

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

so the roots are easy to find in the case that $\alpha \beta - \gamma=0$