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Re: FindRoot

• To: mathgroup at smc.vnet.net
• Subject: [mg98744] Re: [mg98693] FindRoot
• From: Bob Hanlon <hanlonr at cox.net>
• Date: Fri, 17 Apr 2009 04:30:30 -0400 (EDT)
• Reply-to: hanlonr at cox.net

eqn = x^3 - 4 a^2 x - 2 a^3 == 0;

r = Simplify[x /. Solve[eqn, x], a > 0]

{((4*3^(1/3) + (9 + I*Sqrt[111])^
             (2/3))*a)/(3^(2/3)*
        (9 + I*Sqrt[111])^(1/3)), 
   (I*(-12 + 4*I*Sqrt[3] + 
           I*3^(1/6)*(9 + I*Sqrt[111])^
               (2/3) + (27 + 3*I*Sqrt[111])^
             (2/3))*a)/(2*3^(5/6)*
        (9 + I*Sqrt[111])^(1/3)), 
   ((12*I - 4*Sqrt[3] - 
           3^(1/6)*(9 + I*Sqrt[111])^
               (2/3) - 
           I*(27 + 3*I*Sqrt[111])^(2/3))*
        a)/(2*3^(5/6)*(9 + I*Sqrt[111])^
          (1/3))}

Plot[r, {a, 0, 5}]


Bob Hanlon

---- Miguel <misvrne at gmail.com> wrote: 

=============
Hi all,
How can I to find the reals roots of a cubic equation in simbolic
form: For example,

Find the roots of
x^3-4a^2x-2a^3==0

where "a" is real and a>0.

Thanks

• Follow-Ups:
  • Re: Re: FindRoot
    • From: DrMajorBob <btreat1@austin.rr.com>
  • Re: Re: FindRoot
    • From: Gerry Flanagan <flanagan@materials-sciences.com>