From: "N.R.Bruin" <nbruin@wi.leidenuniv.nl>
Newsgroups: sci.math
Subject: Re: Equation of degree 3 - rational solution?
Date: Mon, 12 Aug 1996 11:49:49 +0200

Vincent Lefevre wrote:
> 
> Consider the following equation: x^3 + px + q = 0 with p and q rational.
> Suppose that the square root of abs(q^2 + 4p^3/27) isn't a rational number.
> Can a solution of the equation be rational?

Try

x^3-1 if you want a reducible polynomial with nonsquare -discriminant
x^3-2*x-4 if you want a reducible polynomial with the quantity you
mention a nonsquare (which is -discriminant/27)

Greetings,

Nils