Letbe the function [tex] y=f(x) [/tex] is there a test to prove if its roots are real or either has some complex roots?, or in more general cases:(adsbygoogle = window.adsbygoogle || []).push({});

[tex] y=g(x)D^{k}f(x) [/tex] 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:

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

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

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# Real roots

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