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$
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$
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 ... ?