# Inspired by Vieta's Derivatives

Calculus Level 1

The function $f(x) = x^5 + 6x^4 - 18x^3 - 10x^2 + 45x - 24$ has only four distinct roots, each of which is real. Let the four roots be $\alpha,\ \beta,\ \gamma,$ and $\delta,$ in no particular order. Also let $f'(x)$ denote the first derivative of $f(x).$ Evaluate $f'(\alpha)\times f'(\beta)\times f'(\gamma)\times f'(\delta).$

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