Use the applet below to see the x-values of the intersections of the circle and the parabola. Compare with the x-values of the roots of g(x).
Move p (the coefficient on x^2 in g(x)) and see how it effects the circle. Move q (the coeffiecient on x in g(x)) and see how it effects the circle. Move r (the constant of g(x)) and see how it effects the circle. Click the checkbox on g(x) to see the quartic and its roots.