Sum of Roots of Polynomial/Proof 2

Proof
From Viète's Formulas:


 * $\displaystyle a_{n-k} = \left({-1}\right)^k a_n \sum_{1 \mathop \le i_1 \mathop < \dotsb \mathop < i_k \mathop \le n} z_{i_1} \dotsm z_{i_k}$

for $k = 1, 2, \ldots, n$.

The result follows for $k = 1$.