[tricks]
1. For a polynomial f(z) = c_n z^n + c_{n-1}z^{n-1} + \dotsb + c_0 with roots a_1, \dotsc ,\ a_n,

\displaystyle \sum a_i = -\frac{c_{n-1}}{c_n},
\displaystyle \prod a_i = (-1)^n \frac{c_0}{c_n}

2. \displaystyle{f^\prime (z) = f(z) \left( \frac{1}{z-a_1} + \dotsb + \frac{1}{z-a_n} \right)}

Advertisements