Lesson Don't discriminate the DISCRIMINANT!!!!!

Roots of quadratic equations of the form has two types of roots:real, and imaginary.
Roots are obtained through factoring, completing th square, and the quadratic formula!
The quadratic formula has a discriminant. It is the part.
The discriminant plays an important role in predicting the nature of the roots.
If ,the roots are imaginary and unequal
~~~,the roots are real and unequal
~~~,the roots are real and equal.
Imaginary numbers are imaginary because it is the square root of a negative number. And, squaring a number means multiplying to itself. Thus, squaring any real number will produce a positive number and that negative numbers can not have a REAL square root.
The third condition CAN be easily PROVED!
Take note of the quadratic formula again:

and if part is ZERO, then,

And we all know that adding or subtracting zero produces the same number.
Applying it, the roots are the same and equal.