Quadratic Equation Calculator

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Quadratic Equation Calculator

Demo Examples

Introduction to Quadratic Equations

A quadratic equation is a fundamental concept in mathematics with the standard form ax² + bx + c = 0, where a ≠ 0.

Quadratic Formula

x = (-b ± √(b² - 4ac)) / (2a)

Discriminant Information

Δ = b² - 4ac determines the nature of roots:

Δ > 0: Two distinct real roots
Δ = 0: One repeated root
Δ < 0: Two complex conjugate roots

Introduction to Quadratic Equations

A quadratic equation is a fundamental concept in mathematics with the standard form ax² + bx + c = 0, where a ≠ 0.

Quadratic Formula

x = (-b ± √(b² - 4ac)) / (2a)

Discriminant Information

Δ = b² - 4ac determines the nature of roots:

Δ > 0: Two distinct real roots
Δ = 0: One repeated root
Δ < 0: Two complex conjugate roots

Demo Examples Description

x² - 5x + 6 = 0 - Two positive real roots (x = 2, 3)
x² - 4x + 4 = 0 - One repeated root (x = 2)
x² + 1 = 0 - Complex roots (x = ±i)
2x² + 3x - 2 = 0 - One positive, one negative real root