Let α, β, γ are the real roots of the equation x3+ax2+bx+c=0 (a,b,c∈R and a≠0). If the system of equations (in u, v and w) given byαu+βv+γw=0βu+γv+αw=0γu+αv+βw=0has non-trivial solutions, then the value of a2/b is _______.

Equation x3+ax2+bx+c=0 has roots α, β, γ. Therefore,α+β+γ=−aαβ+βγ+γα=bSince the given system of equations has non-trivial solutions, we haveαβγβγαγαβ=0or   α3+β3+γ3−3αβγ=0or   (α+β+γ)α2+β2+γ2−αβ−βγ−γα=0or   (α+β+γ)(α+β+γ)2−3(αβ+βγ+γα)=0⇒  −aa2−3b=0or   a2/b=3