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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
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