If α and β are the roots of equation x2 + αx + β = 0 then find α3 + β3 = ?

Answer: Option A

$$\begin{array}{rl}& x^2\text{ + }\alpha x+\beta =0\\ & \text{Sum of root}\\ & \alpha +\beta =\frac{-\alpha }{1}......(i)\\ & \alpha \beta =\beta ......(ii)\\ & \text{From (i) and (ii)}\\ & \text{Then, }\alpha =1\\ & \text{Then, }\beta =-2\\ & \text{Then value of }\\ & \iff {\alpha }^3+{\beta }^3\\ & =1+{\left(-2\right)}^3\\ & =-7\end{array}$$