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.
by
Aditya Narayan Sharma