Cubic equation's determinant

Algebra Level 3

If \(\alpha , \beta \text{ & } \gamma \) are the roots of the equation

\[x^3 + ax^2 + b = 0\]

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

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