Re: quartic equation
- To: mathgroup at smc.vnet.net
- Subject: [mg108743] Re: quartic equation
- From: Bob Hanlon <hanlonr at cox.net>
- Date: Tue, 30 Mar 2010 04:59:54 -0500 (EST)
soln = Solve[x^4 + a*x^3 + b*x^2 + c*x + d == 0, x];
Length[soln]
4
Looking at the first of the four roots
x /. soln[[1]]
-((1/2)*Sqrt[(1/(3*2^(1/3)))*
(Sqrt[(27*a^2*d - 9*a*b*c + 2*b^3 - 72*b*d +
27*c^2)^2 - 4*(-(3*a*c) + b^2 + 12*d)^3] +
27*a^2*d - 9*a*b*c + 2*b^3 - 72*b*d + 27*c^2)^
(1/3) + (2^(1/3)*(-(3*a*c) + b^2 + 12*d))/
(3*(Sqrt[(27*a^2*d - 9*a*b*c + 2*b^3 - 72*b*d +
27*c^2)^2 - 4*(-(3*a*c) + b^2 + 12*d)^3] +
27*a^2*d - 9*a*b*c + 2*b^3 - 72*b*d + 27*c^2)^
(1/3)) + a^2/4 - (2*b)/3]) -
(1/2)*Sqrt[-((1/(3*2^(1/3)))*
(Sqrt[(27*a^2*d - 9*a*b*c + 2*b^3 - 72*b*d +
27*c^2)^2 - 4*(-(3*a*c) + b^2 + 12*d)^3] +
27*a^2*d - 9*a*b*c + 2*b^3 - 72*b*d + 27*c^2)^
(1/3)) - (2^(1/3)*(-(3*a*c) + b^2 + 12*d))/
(3*(Sqrt[(27*a^2*d - 9*a*b*c + 2*b^3 - 72*b*d +
27*c^2)^2 - 4*(-(3*a*c) + b^2 + 12*d)^3] +
27*a^2*d - 9*a*b*c + 2*b^3 - 72*b*d + 27*c^2)^
(1/3)) + a^2/2 - (-a^3 + 4*a*b - 8*c)/
(4*Sqrt[(1/(3*2^(1/3)))*
(Sqrt[(27*a^2*d - 9*a*b*c + 2*b^3 - 72*b*d +
27*c^2)^2 - 4*(-(3*a*c) + b^2 + 12*d)^3] +
27*a^2*d - 9*a*b*c + 2*b^3 - 72*b*d + 27*c^2)^
(1/3) + (2^(1/3)*(-(3*a*c) + b^2 + 12*d))/
(3*(Sqrt[(27*a^2*d - 9*a*b*c + 2*b^3 - 72*b*d +
27*c^2)^2 - 4*(-(3*a*c) + b^2 + 12*d)^
3] + 27*a^2*d - 9*a*b*c + 2*b^3 -
72*b*d + 27*c^2)^(1/3)) + a^2/4 - (2*b)/3]) -
(4*b)/3] - a/4
Bob Hanlon
---- Leslaw Bieniasz <nbbienia at cyf-kr.edu.pl> wrote:
=============
Hi,
I am totally unexperienced in MATHEMATICA, and I am looking for some
advice. I need to solve a quartic equation symbolically, that is to factor
a fourth order polynomial given in the power base. The coefficients
of the polynomial are complicated expressions of a number of parameters,
and I need to obtain expressions for the roots as functions of these
parameters. Is there any way to do this? I would appreciate if
anybody can send me some simple example code showing how this sort
of problems can be solved.
Leslaw