Quadratic Formula Calculator
Solve any quadratic equation ax² + bx + c = 0. Finds real and complex roots, discriminant, and vertex.
The Quadratic Formula
For an equation of the form ax² + bx + c = 0, the roots are given by: x = (-b ± √(b² - 4ac)) / 2a. The discriminant Δ = b² - 4ac tells us about the roots: Δ > 0 → two distinct real roots; Δ = 0 → one repeated real root; Δ < 0 → two complex conjugate roots.
Coefficients
Equation: ax² + bx + c = 0
a (coefficient of x²)
b (coefficient of x)
c (constant)
Roots
Root x₁
3
Root x₂
2
Discriminant Δ
1
Vertex (h, k)
(2.5, -0.25)
x = (5 ± √1) / 2 → x₁ = 3, x₂ = 2