Reciprocal sum of roots

Level pending

For \(i=1,2...,2014\) let \(\alpha_i\) and \(\beta_i\) be the roots of

\(x^2-2x-i^2-i=0\).

The value of

\(\displaystyle\sum_{i=1}^{2014}\frac{1}{\alpha_i}+\frac{1}{\beta_i}\)

can be expressed as \(-\frac{a}{b}\), where a and b are coprime positive integers.What is the value of b-2014?

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