# This shouldn't be too hard, if you know the shortcut

Algebra Level 5

Let the 2 roots of the equation $x^2-2x-1=0$ be $\alpha$ and $\beta$. If f(x) is a cubic polynomial that satisfies the following conditions, what is the value of f(-2)?

$f(\alpha )=2\alpha ,\quad f(\beta )=2\beta ,\quad f(\alpha +\beta )=2\alpha +2\beta ,\quad f(\alpha \beta )=4$

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