Matrices and Determinants

Let $\alpha$, $\beta$, $\gamma$ be the real roots of the equation, x³ + ax² + bx + c = 0, (a, b, c $\in$ R 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 ${{{a^2}} \over b}$ is