Selecting Real Roots, Again

*To*: mathgroup at smc.vnet.net*Subject*: [mg67104] Selecting Real Roots, Again*From*: "DOD" <dcodea at gmail.com>*Date*: Fri, 9 Jun 2006 01:08:55 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com

I've read the many posts already here about how to get mathematica to select real roots for you, but I have a slightly(very slighty, I thought) different problem ,and I don't know how to get mathematica to do what I want. I want to get the solution for a polynomial of the following form: d x^n + (1-d) x^2 =y so for example, I do Solve[.9 x^10 + .1 x^2 ==y,x] and I get a whole bunch of solution, very good. For my purposes, y lives in the [0,1], as must the solution. So I can see, by hand, which root I want; exactly one root is both real, and has solutions in my inverval. So I want to tell mathematica to: A: look at only solutions x* that are real over y in [0,1] and B: of those solutions, give the one x* that itself lies is [0,1]. So, when I try to do something from reading previous posts, I cannot get it to work: In[24]:= Select[Solve[.9 x^10 + .1 x^2 ==y,x],Element[x/.#,Reals]&] Out[24]= {} or perhaps In[41]:= Select[Solve[.9 x^10 + .1 x^2 ==y,x],Assuming[Element[y,Reals],Eement[x/.#,Reals]]&] Out[41]= {} So How to I tell mathematica to do this?

**Follow-Ups**:**Re: Selecting Real Roots, Again***From:*"Carl K. Woll" <carlw@wolfram.com>