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.


Inspiration.

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