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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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