Viète's Formulas/Examples/Monic Polynomial

Example of Use of Viète's Formulas
Let:

Let $U$ be the set of $N$ roots of equation $\map P x = 0$.

Then:

Proof
Let:


 * $U = \set {x_1, \ldots, x_N}$

Translate Viète's Formulas from notation $a_0$ to $a_N$:

Let $N-k = j$ define a change of index.

Then $k = N-j$.

Apply the change of index: