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polynomial of 7th order, some structure

• To: mathgroup at smc.vnet.net
• Subject: [mg100729] polynomial of 7th order, some structure
• From: Anatoly <anatoly.bourov at gmail.com>
• Date: Thu, 11 Jun 2009 21:44:56 -0400 (EDT)

hi, I have an equation i have been trying to solve, but no amount of
Solve, Reduce or ToRadical seems to produce an answer.

x(1+x^2)^3 == a x^4 +b x^3 +...+e

I know that it has one or three real roots, depending on combinations
of coefficients, with only one root at x>0.  That is the one that I
want, the root that is > 0.
Does anyone have any ideas what I can do?

I can plot the Root[] results, and I can see that it is usually the
same one root from the list, for most coefficient combinations.

Any way i can get the formula without plugging in the values?