November 26, 2012
In my fourth year of teaching quadratics, I've found that the discriminant has been one of the toughest concepts to master for students in all levels of Algebra II.
The graph below has two imaginary [complex] roots that are distinct. The discriminant would be negative. Distinct root means the roots are different.
The graph below has one distinct root at x=1. This root is a real root and also a complex root. 1 is a complex number because it can be written as 1+0i. The discriminant would be zero.
Finally, the scenario that is most familiar to students from past work is this quadratic with two real solutions of 4 and -2. To be sure, these roots are also complex numbers since they are -2+0i and 4+0i. The discriminant would be positive.
To be sure, the discriminant is b^2-4ac. The part under the radical in the quadratic formula.