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Let's consider the following equation where $m,n$ are real numbers:

$ x^3+mx+n=0 $

I need to prove/disprove without calculus that for any real root of the above equation we have that: $ m^2-4 x_1 n \ge 0$

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Suppose that $x_1$ is a real root of the cubic, and consider the quadratic equation $x_1x^2+mx+n=0$. This must have $x_1$ as a real solution, so ... ?

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    in fact, yes, i wanted to know how did you think of it, but now it's clear. The approach is very unusual.2012-07-04