The discriminant is the part of the Quadratic Forumula under the radical. Here is the Quadratic Formula with the discriminant in bold:
x =-b ∓ √b2 - 4ac
2a
for a problem in the form ax2 + bx + c = 0
Why is the discriminant important? Well, calculating it can determine if it is positive, zero or negative. That will determine how many solutions there are for a quadratic equation ax2 + bx + c = 0. Consider the table below:
| Determinant | Solutions? |
|---|---|
| b2 - 4ac > 0 | 2 solutions are Real numbers (roots are Real and unequal) |
| b2 - 4ac = 0 | Repeated, Real number solution (roots are Real and equal) |
| b2 - 4ac > 0 | Solutions are Imaginary numbers, not Real |