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

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