Talk:Descartes' rule of signs

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Mathematics rating:	Stub Class	Low Priority	Field: Algebra
Please update this rating as the article progresses, or if the rating is inaccurate. Click to show/hide comments. Please add to or update the comments to suggest improvements to the article. Geometry guy 00:26, 3 June 2007 (UTC)

pay attention to the last example: it's wrong... --Arirossa 23:19, 7 February 2007 (UTC)

fixed, thanks for spotting. DavidMcKenzie 12:37, 8 February 2007 (UTC)

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)

What does «Multiple roots of the same value are counted separately» mean, exactly? Mariano (talk) 00:31, 8 February 2008 (UTC)

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)

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)

[edit] Proof

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)

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)

[edit] Moved back to "Descartes' rule of signs"

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)