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Re: cubic polynomial

  • To: mathgroup at smc.vnet.net
  • Subject: [mg22710] Re: cubic polynomial
  • From: "ERIK DOFS" <erik.dofs at swipnet.se>
  • Date: Wed, 22 Mar 2000 00:28:14 -0500 (EST)
  • Organization: A Customer of Tele2
  • References: <8aqs6m$ac8@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Dear Elena,
In addition to all suggestions how to find good numeric solutions, I would
like to add a pragmatic approach that gives you the analytic expression that
you wanted:
Mathematica can give very good approximations, e.g when c>1 the roots are
VERY close to
-3c +1/9 -4/(243c), 2*Sqrt(c/3) +4/9 +5/(27*Sqrt(3c)) and -2*Sqrt(c/3)
+4/9 - 5/(27*Sqrt(3c))
and when c is small (say 0< c <0.1) the roots are close to 1+c +4c^3, -2c
+2c^(3/2) and -2c-2c^(3/2).
BTW, what problem does your equation solve?

Regards Erik D.

E.Carletti1 skrev i meddelandet <8aqs6m$ac8 at smc.vnet.net>...
>
>I have a problem: I want to solve this equation:
>
>x^3+(3c-1)(x^2)-4cx-4(c^2)=0 with respect to x.
>
>It has to have a real solution because it is continuous
>in x. c is a positive parameter.
>If i solve it numerically, plugging numbers for c, then it is fine. But
>I would like an analytical solution: in this case i get only one
>solution which should give me a real value for x (the other two are
>imaginary) but
>it has a square root with all negative members (all terms with c, which
>is positive, with a sign - in front of it, so immaginary). How is that
>possible? What procedure does mathematica use to solve cubic expression?
>
>How can I express the expression in a nicer way to get rid of these
>negative terms? My feeling is that the programm is not able to simplify
>the expression for the solution.
>Could you please help me? if I write the expression I find in the paper
>I am writing, noone will believe it is real!
>And even more funny, if I plug number into the solution I find for x, it
>comes the same number as I plug numbers directly into the function I
>want to solve, except for the last part which is an imaginary number
>which shoult tend to zero.
>What is going on?
>
>Thank your for your help
>
>Elena Carletti
>Financial Markets Group
>LSE
>Houghton Street
>London WC2A 2AE
>
>Tel. 0044 (0)20 7955 7896
>Fax 0044 (0) 20 7242 1006
>
>




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