Question

If one root of the equations $ax^2 + bx + c = 0$ and $bx^2 + cx + a = 0 (a, b, c \in R)$ is common, then the value of $\left(\frac{a^{3} + b^{3} + c^{3}}{abc}\right) $ is

Answer 1

Applying condition for common root, we get
$a^3 + b^3 + c^3 = 3abc$
$\Rightarrow \left(\frac{a^{3} + b^{3} + c^{3}}{abc}\right) = 27$