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Solve / NSolve take too much time or fail


Hello,
I'm working with Mathematica (version 5.0) for perhaps 3 month.
And now I have a problem, I try to solve an equation like this:

cf=(a1*x (a2 + a3*x + a^2))/(b1 + b2*x - b3*x^2 + b4*x^3);

w=(1-c1*Sqrt[1-(1-c1^2)*x/c2])^2 / (1-c1)^2;

This is the main equation:

Solve[Numerator[cf]-I d1 w Denominator[cf]==0,x]

And even after hours of working I don't get any solution, whether I
take Solve or NSolve. And I gave a lot of virtual memory free for
Mathematica to work with.

Are there any tricks to help solving difficult polynomial equations
faster (or at all)? I want to get, of course, a set of Root-functions
for x (complex), depending on a1, a2, a3, b1, b2, b3, b4, c1, c2, d1,
so I have no numerical number to start with for the FindRoot-function.
Can anyone help me? Some other equations, not always that different
from this one, could be solved more easily...

Thank you very much!

Thomas Geyer
(tfgeyer at yahoo.com)


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