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From: Kent Holing on 16 Feb 2010 20:16
Again, thanks. Can you find such an equation with 4 real roots?
From: Derek Holt on 17 Feb 2010 08:36
On 17 Feb, 11:16, Kent Holing <K...(a)statoil.com> wrote:
> Again, thanks. Can you find such an equation with 4 real roots?

It depends on what you mean by "such an equation".

Not of degree 6, because there are no transitive groups of degree 6
and order 12 that contain a transposition.

Derek Holt.
From: Kent Holing on 16 Feb 2010 23:59
So, what degree do we need to come up with such an explicit example?
From: Derek Holt on 17 Feb 2010 11:01
On 17 Feb, 14:59, Kent Holing <K...(a)statoil.com> wrote:
> So, what degree do we need to come up with such an explicit example?

Sorry I am losing track! A specific example of what?

Derek Holt.
From: Kent Holing on 17 Feb 2010 01:17
Explicit example:
An irreducible monic equation with integer coefficients
of degree n, Galois group with 2n elements but not dihedral and at least 4 real roots (and both real and complex roots). This means n > 6.
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