What does the discriminant tell me?

A positive discriminant gives two real roots, zero gives one repeated real root, and a negative discriminant gives two complex roots.

Why can coefficient a not be zero?

If a is zero, the x² term disappears and the equation becomes linear rather than quadratic.

The vertex is the parabola's turning point. It is the minimum point when a is positive and the maximum point when a is negative.

Math Calculators

Quadratic Equation Calculator

Solve ax² + bx + c = 0 and find its roots, discriminant and vertex.

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ax² + bx + c = 0

abc

Roots

x₁ = 2

x₂ = 1

Details

Discriminant: 1

Vertex: (1.5, -0.25)

About the Quadratic Equation Calculator

The quadratic equation calculator solves equations in the standard form ax² + bx + c = 0 using the quadratic formula.

It reports both roots, including complex roots when the discriminant is negative, and also calculates the discriminant and the parabola's vertex.

Results update as coefficients change, making it useful for checking algebra homework, exploring graphs and understanding how each coefficient affects a parabola.

Key features

Real and complex roots
Discriminant calculation
Parabola vertex coordinates
Instant results as coefficients change

How to use

1Enter the coefficients a, b and c from your equation.
2Keep a non-zero so the equation remains quadratic.
3Read the two roots, discriminant and vertex coordinates.

Examples

Solve a quadratic

Input: x^2 - 5x + 6 = 0

Output: x = 2 and x = 3

The two roots are the x values where the equation equals zero.

Frequently asked questions

What does the discriminant tell me?: A positive discriminant gives two real roots, zero gives one repeated real root, and a negative discriminant gives two complex roots.
Why can coefficient a not be zero?: If a is zero, the x² term disappears and the equation becomes linear rather than quadratic.
What is the vertex?: The vertex is the parabola's turning point. It is the minimum point when a is positive and the maximum point when a is negative.

Open a related tool to prepare your files or refine the finished result.