Can a cubic that crosses the x axis at three points have imaginary roots? I have a cubic polynomial, $x^3-12x+2$ and when I try to find it's roots by hand, I get two complex roots and one real one. Same, if I use Mathematica. But, when I plot the graph, it crosses the x-axis at three points, so if a cubic crosses the x-axis a three points, can it have imaginary roots, I think not, but I might be wrong.

Since I have not a copy of Mathematica with me right now, I will send a link to the Wolfram Alpha results:
http://www.wolframalpha.com/input/?i=solve+x3%E2%88%9212x%2B2+%3D+0, which are the same as the Mathematica results, since Wolfram Alpha uses Mathematica as a computational engine.
