Zeros of Parabola

In the left Sketch you can control the shape and position of the parabola y = a x2 + b x + c by using the Controllers.

Parabola & Coefficients Zeros in the Complex Plane
[GeoScript-File 1] [GeoStyle-File]

[GeoScript-File 2] [GeoStyle-File]

Problem: How do the eigenvalues change when you change
a and keep the others fixed as b = 1, c = 2?
b and keep the others fixed as a = 1, c = 2?