Re: Roots of x^3 = 1;

From: The Fiendish Plot of Fascinet (fascinet_at_yahoo.com)
Date: 10/27/04 

Date: 27 Oct 2004 14:15:43 -0700

Gib Bogle <bogle@ihug.too.much.spam.co.nz> wrote in message news:<clngvb$1n4$1@lust.ihug.co.nz>...
> Saju wrote:
>
> > Hello,
> >
> > I was teaching myself some algebra when I got stuck at the following
> > ...
> >
> > I am trying to find roots of x^3 = 1
> >
> > x =1 is a solution. But keeping x = i^(4/3) also seems to work, so
> > does i^(8/3), i^(16/3) and so on - I am able to generate 1 real root
> > and infinite complex roots - this must be bogus.
> >
> > According to the theory, x^3 = 1 must have 3 roots (real+complex) - so
> > what am I missing ?
> >
> > regards
> > srp
>
> 1 = e^2nxi (where x = pi), for n = 0,1,2,3,...
>
> 1^(1/3) = e^(2nxi/3), for n = 0,1,2,3,...
>
> This takes values that are points on the unit circle in the complex
> plane with argument 0, 2x/3, 4x/3 for n = 0,1,2 (for higher values of n
> these values are repeated). The first value is of course 1, the other
> two are complex.
>

Is there any easy way to get the real roots out of a quartic or a
quintic polynomial?

-F

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