       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:=
Select[Solve[.9 x^10 + .1 x^2 ==y,x],Element[x/.#,Reals]&]

Out=
{}
or perhaps
In:=
Select[Solve[.9 x^10 + .1 x^2
==y,x],Assuming[Element[y,Reals],Eement[x/.#,Reals]]&]
Out=
{}

So How to I tell mathematica to do this?

```

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