finding roots of 1 + 6*x - 8*x^3

*To*: mathgroup at smc.vnet.net*Subject*: [mg54630] finding roots of 1 + 6*x - 8*x^3*From*: "Kennedy" <kennedy at oldnews.org>*Date*: Thu, 24 Feb 2005 03:21:35 -0500 (EST)*Sender*: owner-wri-mathgroup at wolfram.com

Hello All, I am trying to find the roots of 1 + 6*x - 8*x^3. Roots[1+6*x-8*x^3==0,x] yields this ugly thing: (made uglier by my converting to InputForm) x == ((1 + I*Sqrt[3])/2)^(1/3)/2 + 1/(2^(2/3)*(1 + I*Sqrt[3])^(1/3)) || x == -((1 - I*Sqrt[3])*((1 + I*Sqrt[3])/2)^(1/3))/4 - ((1 + I*Sqrt[3])/2)^(2/3)/2 || x == -(1 - I*Sqrt[3])/(2*2^(2/3)*(1 + I*Sqrt[3])^ (1/3)) - (1 + I*Sqrt[3])^(4/3)/(4*2^(1/3)) This monstrosity is chock full of imaginaries, even though I know all three roots are real. I tried Solve too but got the same thing, except in the form of a set of replacements. My guess is that Solve just calls Roots when handed a poly- nomial. When I ran the above through FullSimplify, I got three "Root" objects, the upshot of which is that the roots of the polynomial are indeed the Roots of said polynomial. Huh. What command can I use to get the roots into a form that are (a) purely real, and (b) in radical form? Thanks, Kennedy PS. Mathematica 4.2

**Follow-Ups**:**Re: finding roots of 1 + 6*x - 8*x^3***From:*Andrzej Kozlowski <akoz@mimuw.edu.pl>

**Re: finding roots of 1 + 6*x - 8*x^3***From:*Murray Eisenberg <murray@math.umass.edu>

**Re: finding roots of 1 + 6*x - 8*x^3***From:*Daniel Lichtblau <danl@wolfram.com>