Vieta's Derivatives

Algebra Level 4

\[f(x)=x^{3}-x^{2}-2x+1\]

Let the zeros of the function above be \(\alpha,\beta,\) and \(\gamma. \)

Find \( f'(\alpha)\times f'(\beta)\times f'(\gamma). \)

Note: \(f'(x)\) denotes the derivative of \( f(x).\)

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