Roots Revisited

Algebra Level 5

A polynomial f(x)f(x) of degree nn with real coefficients has roots x1,x2,,xn1x_1, x_2, \ldots , x_n\ne1 is such that f(1)=10f(1)=-10, f(1)=1f'(1)=1 and f(1)=6f''(1)=6.

Find i=1n1(1xi)2\displaystyle \sum_{i=1}^{n}\dfrac{1}{(1-x_i)^2}.

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


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