Let $\alpha, \beta, \gamma$ be the real roots of the equation $x^3 + ax^2 + bx + c = 0$, $(a, b, c \in \mathbb{R} \text{ and } a, b \ne 0)$. If the system of equations (in $u, v, w$) given by $\alpha u + \beta v + \gamma w = 0$, $\beta u + \gamma v + \alpha w = 0$, $\gamma u + \alpha v + \beta w = 0$ has non-trivial solution, then the value of $\dfrac{a^2}{b}$ is: