10 - Quadratics and Complex Numbers

A quadratic is an equation of form

Oh, the classic.
The determinant determines how many real roots this equation has. What you did in high school was that if this determinant was positive, there were two real roots.

If this determinant is zero, there are two real roots which have the same value

And, if this determinant is negative, it has no solutions in R.

That's because the solutions are complex!

And exactly, these complex roots are a conjugate pair. They are complex conjugates of each-other.