Discriminant
MathDefinition
The discriminant is the expression b² - 4ac from the quadratic formula, and it determines the number and type of solutions of a quadratic equation ax² + bx + c = 0. A positive discriminant gives two real solutions, zero gives one real solution, and a negative discriminant gives two complex solutions.
Examples
- For x² - 5x + 6 = 0: discriminant = 25 - 24 = 1 (two real solutions)
- For x² + 4 = 0: discriminant = 0 - 16 = -16 (two complex solutions)
- For x² - 6x + 9 = 0: discriminant = 36 - 36 = 0 (one repeated solution)
Key Fact
Δ = b² - 4ac: Δ > 0 → 2 real roots; Δ = 0 → 1 repeated root; Δ < 0 → 2 complex roots
Study This Concept
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