Talk:Descartes' rule of signs

message: pay attention to the last example: it's rong... --Arirossa 23:19, 7 February 2007 (UTC)
replies: text: fixed, thanks for spotting. DavidMcKenzie 12:37, 8 February 2007 (UTC)
replies: text: Actually, it was correct before "fixing". The factorization and roots discussed in the final lines refer to the original polynomial, not the sign-flipped version. --mglg(talk) 16:42, 13 February 2007 (UTC)

text: Take (x + 1)^{2}(x - 1) this polynomial has two roots with the value x=-1, and one with value x=1. So counting roots we have 2 negative roots and one positive root. --Salix alba (talk) 00:46, 8 February 2008 (UTC)
replies: text: Wouldn't the very much more standard ``Roots are counted taking into account their multiplicities be better? Mariano (talk) 18:33, 15 February 2008 (UTC)

message: The example is all well and good, but it's not a proof.
I happen to know that the proof is rather long, so perhaps it would be apt to provide an external link to it, if anyone can find it.
Thanks, Glooper 20:24, 3 November 2007 (UTC)
replies: text: There seem to be a few neat expositions of various proofs floating around, I added the one from Cut the Knot since they cater for most audiences. Chenxlee (talk) 14:25, 20 February 2008 (UTC)

text: @GlooperGlooper and @Chenxlee The proof is clearly lacking.  I have neither the time nor the inclination to fix it.  I will add words similar to "A rough outline or sketch of the proof follows." Nickalh (talk) 11:17, 11 October 2023 (UTC)
thread_title:  Proof 

message: I have reversed the recent move to "Descartes's rule of signs". The usual possessive form of Descartes is Descartes' - this is the standard followed on other sites such as MathWorld and the Stanford Encyclopedia of Philosophy, and in the titles of books such as Descartes' Error and Descartes' Metaphysical Physics. Gandalf61 (talk) 16:53, 5 February 2008 (UTC)
thread_title:  Moved back to "Descartes' rule of signs" 

message: "This polynomial has two sign changes, meaning the original polynomial has 2 or 0 negative roots and this second polynomial has 2 or 0 positive roots."
Aren't the positive roots counted from the original polynomial and the negative roots from the second?
--Patrick McLaren (talk) 22:56, 15 October 2010 (UTC)
thread_title:  Second Example 

message: The page lacks a proof; please put it in. 76.181.64.113 (talk) 20:02, 21 July 2011 (UTC)
replies: text: Wikipedia is an encyclopedic reference, not a textbook. To see a proof you can follow the link under External links or consult an algebra textbook. Gandalf61 (talk) 09:34, 22 July 2011 (UTC)
thread_title:  Comment 

message: Here is a source for Descartes Geometrie: http://www.gutenberg.org/ebooks/26400 The rule is on page 42. Maybe this is interesting: Descartes also makes the statement that you can determine the number of negative roots (called "false" by Descartes) by counting unchanging signs between consecutive coefficients. Descartes does not say what to do with coefficients that are zero, but you have to insert an arbitrary sign for any zero to make the rules work. Another point: Descartes is talking only about polynomials with all real roots.  — Preceding unsigned comment added by 93.220.47.168 (talk) 17:56, 11 May 2014 (UTC)
thread_title:  Original source + unchanging signs