SAT and ACT math terms · SAT Math, ACT Math
Discriminant
Discriminant: The expression b² − 4ac in a quadratic equation ax² + bx + c = 0, which tells how many real solutions the equation has.
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What it means
If b² − 4ac > 0, there are two distinct real solutions. If it equals 0, there is exactly one real solution (a repeated root). If it is negative, there are no real solutions. The discriminant is the part under the square root in the quadratic formula, x = (−b ± √(b² − 4ac)) / (2a).
It is also useful for finding when a line and a parabola intersect, by setting them equal and checking the discriminant of the resulting quadratic.
Example
For x² − 6x + 9 = 0, b² − 4ac = 36 − 36 = 0, so there is exactly one solution, x = 3.
On the exam
SAT questions often ask for the value of a constant that gives exactly one or no real solutions.