Roots Revisited

Algebra Level 5

A polynomial $f(x)$ of degree $n$ with real coefficients has roots $x_1, x_2, \ldots , x_n\ne1$ is such that $f(1)=-10$ , $f'(1)=1$ and $f''(1)=6$ .

Find $\displaystyle \sum_{i=1}^{n}\dfrac{1}{(1-x_i)^2}$ .

Clarification: $f'(x)$ and $f''(x)$ represents the first and second derivative of $f(x)$ , respectively.

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