Talk:Complex conjugate root theorem

generalization?

maybe one could mention that the same theorem applies to an analytic function whose series has real coefficients (but the result is restricted to the part of the domain where the series represents the function). Lunch 21:20, 30 January 2007 (UTC)[reply]

comment from the AfD

there was a comment on the AfD that caught my eye:

Keep. In the future, this page could maybe be renamed into "Properties of polynomial roots". (This would solve the google test and the somewhat clumsy name. See above comment by ais523.) In addition to the complex conjugate property, such a page could also disucss: 1) how roots depend continuously but not differentiably on the coefficients, 2) bounds on the roots in terms of the coefficients. There are probably many other properties of polynomials that merit a discussion. Haseldon 18:55, 30 January 2007 (UTC)

one could also throw in such trivia as: the convex hull of the roots of a polynomial contains the roots of the derivative of the polynomial. (with the corollary that if a polynomial's roots all have positive real part, then so do the roots of all its derivatives.)

cheers, Lunch 17:27, 31 January 2007 (UTC)[reply]

As a start I created Properties of polynomial roots. There is still lots of work though. Haseldon 19:33, 31 January 2007 (UTC)[reply]