Let α,β,γ be 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 by  αu+βv+γw=0βu+γv+αw=0γu+αv+βw=0 has 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 haveα0βγβγαγαβ=0 or α3+β3+γ3−3αβγ=0 or (α+β+γ)α2+β2+γ2−αβ−βγ−γα=0 or (α+β+γ)(α+β+γ)2−3(αβ+βγ+γα)=0⇒−aa2−3b=0  or  a2/b=3