Discriminant
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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 x-intercepts, associated with a quadratic equation. 

There are three situations:

Value of the discriminant Example showing nature of roots of ax2 + bx + c = 0 Graph indicating x-intercepts
y = ax2
+ 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 x-intercepts.

ZERO




There is one real root.
(The root is repeated.)


There is one x-intercept.

NEGATIVE


There are two complex roots.
 


There are no x-intercepts.