If α, β, γ are the roots of px3+qx2+r=0, then the value of the determinant αβ    βγ    γαβγ    γα    αβγα    αβ    βγ is

Operation C1→C1+C2+C3 gives(αβ+βγ+γα)1βγγα1γααβ1αββγFrom the given equation, αβ+βγ+γα=0. So, the value of determinant is 0.