# Real roots

1. Nov 5, 2006

Letbe the function $$y=f(x)$$ is there a test to prove if its roots are real or either has some complex roots?, or in more general cases:

$$y=g(x)D^{k}f(x)$$ k>0 and a real D=d/dx number.

The cuestion is that sometimes it can be very deceiving to tell if a function has real or complex root, for example:

$$y=exp(2 \pi x)-1$$ has only real roots.. but for real x the function is complex

$$y=exp(x^2)+1$$ has only complex roots ,but for every real x the function is real.