If α, β, γ are the roots of x3+b x+c=0, then the determinant Δ=|α β γ β γ α γ α β| equals

Question

If α, β, &gamma; are the roots of x3+b x+c=0, then the determinant Δ=|α β &gamma; β &gamma; α &gamma; α β| equals (A) -b3 (B) b3-3 c (C) b2-3 c (D) 0

Tardigrade Admin · Accepted Answer

In this case α+β+&gamma;=0. Thus, from (1) in solution to question 26 , we get Δ=0.

Q. If $α, β, γ$ are the roots of $x^{3} + b x + c = 0$ , then the determinant $Δ = ∣ ∣ α β γ β γ α γ α β ∣ ∣$ equals