Number of roots from Solve?

*To*: mathgroup at smc.vnet.net*Subject*: [mg48423] Number of roots from Solve?*From*: Goyder Dr HGD <h.g.d.goyder at cranfield.ac.uk>*Date*: Sat, 29 May 2004 03:06:44 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com

I am working with the expression a =.; b =.; e = (1/z)((2 + z^2 (b - 1))/(b + 1))^((1 + b)/(2(b - 1))) and was not surprised to find a number of complex and real roots (6) for the particular case a = 10.; b = 1.4; s = Solve[a == e]; {Length[s], s} I was surprised that the number of roots changed to 41 for the case a = 10.; b = 1.05; s = Solve[a == e]; {Length[s], s} With a = 10.; b = 1.03; s = Solve[a == e]; {Length[s], s} I never got an answer (or the calculation takes longer than my patience). Is it possible to predict the number of roots that an expression like e above will produce? Does Mathematica find all the roots, particularly as we are dealing with approximate numbers? Many thanks Hugh Goyder -- This message has been scanned for viruses and dangerous content by the Cranfield MailScanner, and is believed to be clean.

**Follow-Ups**:**Re: Number of roots from Solve?***From:*Andrzej Kozlowski <akoz@mimuw.edu.pl>