$f(x)=(x^3 -3x)^2 - x-2$
Well, I was trying to find the roots of this polynomial of degree $6$ and, after a look at WolframAlpha I noticed something strange. According to Wolfram, there are $3$ real roots and $3$ complex non-real roots. How is this possible, since, because of Conjugate Complex Root Theorem, there always have to be an even number of them?
I can see that the plot shows $6$ intersections with the $x$-axis, then probably this is a problem with Wolfram indeed...
I guess the solutions are computed with floating point arithmetic and there are some rounding errors. The imaginary parts are $10^{-16}$ and $5\cdot 10^{-17}.$
(Maple gives the roots as exact radicals, but if you convert to floating point you get imaginary parts of order $10^{-d},$ where $d$ is the number of digits in the computation.)