# Roots of a 100-th degree polynomial

Algebra Level 5

$\large f(x)=x^{100}+a_{99}x^{99}+\ldots+a_{1}x+a_{0}$

Let $$f(x)$$ be a 100th degree polynomial such that $$a_{99}=-10,$$ $$a_{98}=5$$ and $$a_{97}=-2$$ with roots $$x_{1}, x_{2}, x_{3}, \ldots x_{100}$$. Evaluate$$\displaystyle \sum_{k=1}^{100} x_{k}^3$$.

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