Let \(\alpha, \beta, \gamma\) be the real roots of the equation, \(x^3+a x^2+b x\) \(+c=0,(a, b, c \in R\) and \(a, b \n…

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

[JEE Main 2021, 18 Mar (Shift 1)]