Conjectures about Complex roots of polynomials

In the right hand panel the function x^2 + Px + Q is plotted over the complex plane The left hand panel shows the (P, Q) plane. The coordinates of the large dot determine the values of P and Q. Varying the values of P and Q allow you to explore the real and complex roots of the quadratic. Why does the dot change color? Where is it red? green? Can you make a conjecture about a similar construction for cubics? Can you prove it?