# [Maxima] Solving polynomials with Maxima ?

Richard Fateman fateman at cs.berkeley.edu
Mon Sep 22 17:16:36 CDT 2008

```Your "polynomial" is of degree 3 in x^(1/2).

I suggest you make the change of variables t=x^(1/2) and solve

a*t^3-b*t^2+c*t-d=0.

This can be solved for t by solve(......,t);

then take the square root of the answer. This will give you 6 solutions (+
and - sqrt).

I hope this helps.

(The symbolic solution to a cubic like this is generally very complicated
and not of much use.)

_____

From: maxima-bounces at math.utexas.edu [mailto:maxima-bounces at math.utexas.edu]
On Behalf Of Laure.DUTOIT at cepal.org
Sent: Monday, September 22, 2008 3:10 PM
To: maxima at math.utexas.edu
Subject: [Maxima] Solving polynomials with Maxima ?

Dear all,

I am trying to solve a polynomial using Maxima, but I cannot get an explicit
answer. My polynomial is of the following form:
x^(3/2) a - x b + x^(1/2) c - d =0, where a,b,c and d are composed of
several variables, but are not of interest.

So, I would like to be able to solve this polynomial (I am not a
mathematician, but I think solving such a polynomial is feasible using a
mathematical software, no ?) using Maxima to get to an answer of the form
x=f(a,b,c,d) and not x=f(a,b,c,d,x), as I now get using the command "solve"
(i.e, the answer I am given is not explicit).

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