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

Roots of quadratic equations of the form ax^2+bx+c=0

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 b^2+4*a*c

part.
The discriminant plays an important role in predicting the nature of the roots.
If b^2+4*a*c<0

,the roots are imaginary and unequal
~~~ b^2+4*a*c>0

,the roots are real and unequal
~~~ b^2+4*a*c=0

,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:
x = (-b +- sqrt( b^2-4*a*c ))/(2*a)

and if

part is ZERO, then,
x=(-b+-0)/(2*a)

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