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MathGroup Archive 2004

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RE: Exact real solutions of cubic equations

  • To: mathgroup at
  • Subject: [mg46989] RE: [mg46932] Exact real solutions of cubic equations
  • From: JonasB at
  • Date: Fri, 19 Mar 2004 01:35:38 -0500 (EST)
  • Sender: owner-wri-mathgroup at

Thank you all. Within 24 hours I had 10 answers to my question
(ComplexExpand), with pointers to the theory and a bit of history. As a
newcomer to this list, I am impressed.


> -----Original Message-----
> From: JonasB at [mailto:JonasB at] 
To: mathgroup at
> Sent: den 17 mars 2004 01:55
> To: mathgroup at
> Subject: [mg46989] [mg46932] 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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