150 Friends Problem

Algebra Level 5

\[\large f(x)= x^{150} + x^{2} -7x + 1\]

Let \(x_{1}\), \(x_{2}\), \(x_{3}\)\(\ldots\) \(x_{150}\) be the roots of the above equation. Define

\[\large S = \huge \sum_{i=1}^{150}\dfrac{1}{(1+x_{i})^{2}}\]

Find \( |S| \).

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