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Real roots

  1. Nov 5, 2006 #1
    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:

    [tex] y=g(x)D^{k}f(x) [/tex] k>0 and a real D=d/dx number.:rolleyes: :rolleyes:

    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.
  2. jcsd
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