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?