52 · Calculators

Quadratic Equation Solver

Enter a, b and c to get the solutions of ax² + bx + c = 0, real or complex.

Solves ax² + bx + c = 0.

Solutions

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How to use the quadratic equation solver

  1. Write your equation in the form ax² + bx + c = 0.
  2. Enter a, b and c, including minus signs.
  3. Read the solutions.

The quadratic formula

x = (−b ± √(b² − 4ac)) ÷ 2a. The part under the root, the discriminant, tells you what to expect: positive means two real roots, zero means one, negative means two complex roots.

Examples

x² − 3x − 10 = 0

x = 5 or x = −2

x² + 2x + 5 = 0

x = −1 ± 2i

Questions

What if a is 0?

Then it’s a linear equation, bx + c = 0, and the solver gives its single answer.

What is the vertex?

The turning point of the parabola y = ax² + bx + c.