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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