Cubic equation's determinant

Algebra Level 4

If α,β & γ\alpha , \beta \text{ \& } \gamma are the roots of the equation

x3+ax2+b=0x^3 + ax^2 + b = 0

find the value of αβγβγαγαβ\begin{vmatrix} \alpha & \beta & \gamma \\ \beta & \gamma & \alpha \\ \gamma & \alpha & \beta \\ \end{vmatrix} .

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