Vieta's Formulas
Background
Let ,
where the coefficient of
is
. As a consequence of the Fundamental Theorem of Algebra, we can also write
![$P(x)=a_n(x-r_1)(x-r_2)\cdots(x-r_n)$](http://latex.artofproblemsolving.com/1/c/0/1c0ce6bdc6364145297d8e3473ea84a0937c2600.png)
where are the roots of
.
Let be the
th symmetric sum.
Statement
, for
.
Proof
[needs to be added]