Floored roots

Calculus Level 2

\[\large{x^3+x^2-5x-1=0}\]

Let \(\alpha,\beta,\gamma\) be the roots of the equation above.

Evaluate \(\left\lfloor \alpha \right\rfloor +\left\lfloor \beta \right\rfloor +\left\lfloor \gamma \right\rfloor \).

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