In this cubic, all three roots are real, but cannot be expressed with
real radicals, even in principle. See
http://en.wikipedia.org/wiki/Casus_irreducibilis . They *can* be
expressed as real expressions involving trigonometric functions, which
is what rectform does for you.
That said, I wonder why you want the roots expressed as symbolic
expressions. I suppose there must be some application where
(8*cos(atan(sqrt(2101)/(69*sqrt(3)))/3)-sqrt(3))/sqrt(3) is more
useful than 3.584428340330492, but usually the latter is what you
really want, in which case why not calculate it directly using
realroots or allroots (which, unlike solve, work for *all*
polynomials, not just those which reduce to the quartic case or
simpler by factorization or polynomial decomposition).
-s
On Fri, Apr 17, 2009 at 10:34 AM, Raymond Toy
<raymond.toy at stericsson.com> wrote:
> solve(A^3+3*A^2-13*A-38=0,A);