The discriminant is the name given to the expression that appears under
the square root (radical) sign in the quadratic formula.

Quadratic Formula:

Discriminant


The discriminant tells you about the "nature" of the roots
of a quadratic equation given that a, b and c are rational numbers.
It quickly tells you the number of real roots, or in other words, the
number of xintercepts, associated with a quadratic equation.
There are three situations:
Value of the discriminant 
Example showing nature of roots of ax^{2
}+ bx + c = 0 
Graph indicating xintercepts
y = ax^{2 }+
bx + c 
POSITIVE

There
are two real roots.
(If the discriminant is a perfect
square, the two roots are rational numbers. If the
discriminant is not a perfect square, the two roots are
irrational numbers containing a radical.) 
There are two xintercepts. 
ZERO 
There is one real root.
(The root is repeated.)

There is one xintercept.

NEGATIVE 
There
are two complex roots.

There are no xintercepts. 