How can you tell an equation's real or imaginary roots just from its graph, without knowing the equation? I have to look ath the graph of a parabola, absolute value, and a negative third degree equation and do so? Are there any links that could explain this as I can't scan in the problems to show you? Or could you just make a generalization?

Question

bobpursley · Answer

You can make a generalization, but it involves Riemann surfaces, and you are not ready for that.

Look at this, and you will get an inkling. Everywhere a graph crosses the x axis is a real root, however, everwhere there is a minimum as in this graph, you can do this trick to pull out a pair of complex roots.
http://www.math.hmc.edu/funfacts/ffiles/10005.1.shtml