Discriminant
See It in Action
Two examples of the idea done right—and one common look-alike that is not right.
EXAMPLE
EXAMPLE
NON-EXAMPLE
Definition
The discriminant refers to the part of the quadratic formula that helps determine the nature of the solutions to a quadratic equation. The discriminant is the expression under the square root in the quadratic formula:
The discriminant is the part b^2 - 4ac.
The value of the discriminant gives you important information about the types of solutions the quadratic equation has:
1. If the discriminant is positive (b^2 - 4ac > 0), there are two real and distinct solutions.
2. If the discriminant is zero (b^2 - 4ac = 0), there is one real solution (or a repeated real solution).
3. If the discriminant is negative (b^2 - 4ac < 0), there are no real solutions, but there are two complex (imaginary) solutions.
In summary, the discriminant helps you quickly determine whether a quadratic equation will have two real solutions, one real solution, or no real solutions.