Quadratic Formula Solver
Solve ax² + bx + c = 0 — real and complex roots, discriminant, and vertex.
Equation: 0x² + 0x + 0 = 0
The quadratic formula
For ax² + bx + c = 0, the solutions are: x = (−b ± √(b²−4ac)) ÷ (2a). The expression b²−4ac is called the discriminant. If it's positive, there are two distinct real roots. If zero, one repeated real root. If negative, two complex (imaginary) roots.
Frequently asked questions
What are complex roots?
When the discriminant is negative, the square root of a negative number is involved. The roots are complex numbers of the form a + bi, where i = √(−1). Complex roots always come in conjugate pairs (a + bi and a − bi).
What is the vertex of a parabola?
The vertex is the minimum (or maximum) point of the parabola y = ax² + bx + c. Its x-coordinate is −b/(2a) and its y-coordinate is found by substituting back into the equation. The vertex x-coordinate is also the average of the two roots.
