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Exact real solutions of cubic equations


Hello,

I would like to find the _exact_ real roots of some cubic polynomials.
Mathematica seems to have problems determining that a root is real
 
Solve[1 + a s + b s^2 + s^3 == 0, s]

results in three complex solutions for a = -4 and b = 3. FullSimplify does
not help, either it does nothing or it gets stuck, depending on the values
of a and b. I can of course evaluate the solution numerically, but that is
not what I want. Does anyone know of a package that can simplify expressions
with complex numbers? 

Jonas


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