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 $|S|$ .