I can't seem to find a good resource on Vieta's root jumping, which would explain various scenarios that suggest using the technique.
Does anyone have a suggestion for a reference?
EDIT: start with THIS
The nontrivial use of this is in the Markov spectrum. See CUSICK and FLAHIVE. Kap and I found a number of other trees and related problems, see KAP PDF . Hurwitz expanded Markov's original tree in three variables to $n$ variables about 1907, see info in http://mathoverflow.net/questions/84927/conjecture-on-markov-hurwitz-diophantine-equation . The result becomes a forest rather than a single tree for some $n \geq 14.$ Many related problems are possible, as the term $a x_1 x_2 \ldots x_n$ can be replaced by any homogeneous symmetric polynomial as long as the exponent on each $x_i$ is 1 and the total degree of each term is at least 3.
Yimin Ge has written a short note, http://www.yimin-ge.com/doc/VietaJumping.pdf
Project Pen also had a short piece on IMO 1988 number 6, http://projectpen.files.wordpress.com/2008/10/pen-vol-i-no-1.pdf