Difference between revisions of "Vieta's Formulas"
m |
m (→Statement: fixed spacing) |
||
Line 8: | Line 8: | ||
=== Statement === | === Statement === | ||
− | |||
− | for <math>{}1\le k\le {n}</math>. | + | <math>\sigma_k = (-1)^k\cdot \frac{a_{n-k}}{a_n{}}</math>, for <math>{}1\le k\le {n}</math>. |
=== Proof === | === Proof === | ||
[needs to be added] | [needs to be added] |
Revision as of 16:49, 18 June 2006
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]