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RE: cubic polynomial

  • To: mathgroup at smc.vnet.net
  • Subject: [mg22664] RE: [mg22646] cubic polynomial
  • From: "Harvey P. Dale" <hpd1 at is2.nyu.edu>
  • Date: Sat, 18 Mar 2000 01:27:41 -0500 (EST)
  • Sender: owner-wri-mathgroup at wolfram.com

Elena:
	Here's a work-around to your problem: use other constants in lieu of
those stated, e.g., x^3 + m x^2 - n x - p.  Then Solve the cubic for x.
Then substitute in the patterns you originally intended, for example,
<solution> /. m->(3c-1).  At the end of the process, you'll have solutions
in which the only constant is c.
	This is quite inelegant, I know, but it seems to work fine.
	Harvey Dale

 -----Original Message-----
From: 	E.Carletti1 [mailto:E.Carletti1 at lse.ac.uk] 
To: mathgroup at smc.vnet.net
Sent:	Thursday, March 16, 2000 9:11 AM
To:	mathgroup at smc.vnet.net
Subject:	[mg22646] cubic polynomial


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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