# 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?

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