Let $\alpha, \beta, \gamma$ be the real roots of the equation, $\mathrm{x}^2+\mathrm{ax}^2 +b x+c=0,(a, b, c \in R$ and $a, b \neq 0)$, If the system of equations (in $u, v, w$ ) given by $\alpha u+\beta v+ \gamma \mathrm{w}=0, \beta \mathrm{u}+\gamma \mathrm{v}+\alpha \mathrm{w}=0 ; \gamma \mathrm{u}+\alpha \mathrm{v}+\beta \mathrm{w}=0$ has non-trivial solution, then the value of $\frac{a^2}{b}$ is