Roots of a 100-th degree polynomial

Algebra Level 5

f(x)=x100+a99x99++a1x+a0\large f(x)=x^{100}+a_{99}x^{99}+\ldots+a_{1}x+a_{0}

Let f(x)f(x) be a 100th degree polynomial such that a99=10,a_{99}=-10, a98=5a_{98}=5 and a97=2a_{97}=-2 with roots x1,x2,x3,x100x_{1}, x_{2}, x_{3}, \ldots x_{100}. Evaluatek=1100xk3\displaystyle \sum_{k=1}^{100} x_{k}^3.

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