Talk:Viète's Formulas

19 October 2019

 * The 'Proof' is an outline of a proof. If foils is changed to expands then it is fixed enough for an outline of a proof. Does anyone care that there is no proof?

29 October 2019
Viète Theorem is stated for commutative rings with unity. The proof uses linear independence of the powers $x^k$. Currently, I found on proofWiki no ring theory support for such independence arguments.
 * Suggestion: replace commutative ring with unit by the set $R$ of real numbers. ProofWiki section Corollary efficiently handles ring theory extensions.

The state of the page after edits for correct definitions and references, which breaks the proof Viète's Formulas except for real numbers:

Viète Theorem
Let
 * $\map P x = a_n x^n + a_{n - 1} x^{n - 1} + \dotsb + a_1 x + a_0$

be a polynomial of degree $n$ over a commutative ring with unity $R$.

Suppose $a_n$ is invertible in $R$ and:
 * $\displaystyle \map P x = a_n \prod_{k \mathop = 1}^n \paren {x - z_k}$

where $z_1, \ldots, z_k \in R$ are roots of $P$, not assumed unique.

Then:

Listed explicitly: