How it is calculated
Δ = b² − 4ac x = (−b ± √Δ) ÷ 2a- Δ > 0: two distinct real roots.
- Δ = 0: one repeated root x = −b/2a.
- Δ < 0: no real roots; two complex roots.
Vertex of the parabola: (−b/2a , −Δ/4a).
Worked example
x² − 5x + 6 = 0: Δ = 25 − 24 = 1, so x = (5 ± 1) ÷ 2: x = 3 and x = 2; factored (x − 2)(x − 3).
Frequently asked questions
What if a = 0?
It becomes linear: bx + c = 0 with x = −c/b.
What are complex roots?
Numbers p ± qi where i² = −1, appearing when the discriminant is negative.
Sum and product of roots?
Sum = −b/a and product = c/a (Vieta’s formulas).