math

Quadratic Equation

A second-degree polynomial equation of the form ax² + bx + c = 0, where a ≠ 0.

A quadratic equation graphs as a parabola and has at most two solutions (roots).

The Quadratic Formula

x = (−b ± √(b² − 4ac)) / 2a

The Discriminant (Δ = b² − 4ac)

  • Δ > 0: Two distinct real roots
  • Δ = 0: One repeated real root
  • Δ < 0: Two complex (imaginary) roots

Example

2x² + 5x − 3 = 0 → x = (−5 ± √(25+24)) / 4 = (−5 ± 7) / 4 → x = 0.5 or x = −3

Related Calculators

Related Terms