I just wanted to say first of all that I am not looking for any specific answers, just hoping someone could shed a light on the subjects at hand. Is the quadratic formula a specific example of some general root finding algorithm that solves for the n (or n-1?) roots of a nth degree polynomial? Kind of like the Pythagoras theorem is a specific example of the law of cosines for right triangles? How do I understand those concepts intuitively? Should I learn complex analysis to get how the complex roots work out?