Quadratic Equation Calculator | Free Online Solver

Free online quadratic equation calculator. Solve quadratic equations, find roots, vertex, and discriminant. Step-by-step solutions with detailed explanations.

Solve Quadratic Equations

Understanding Quadratic Equations

The Quadratic Formula

x = (-b ± √(b² - 4ac)) / (2a)

Where ax² + bx + c = 0 is the standard form of a quadratic equation

Key Components

  • • Discriminant (b² - 4ac)
  • • Coefficient of x² (a)
  • • Coefficient of x (b)
  • • Constant term (c)

Types of Roots

  • • Real and Distinct (discriminant > 0)
  • • Real and Equal (discriminant = 0)
  • • Complex (discriminant < 0)

Real-world Applications

Physics

Projectile motion, gravitational fields, and wave equations

Engineering

Structural analysis, electrical circuits, and fluid dynamics

Economics

Supply and demand curves, profit optimization

Frequently Asked Questions

What is a quadratic equation?

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

How do you solve a quadratic equation?

Quadratic equations can be solved using the quadratic formula, factoring, or completing the square. Our calculator uses the quadratic formula for precise results.

What does the discriminant tell us?

The discriminant (b² - 4ac) determines the nature of roots. Positive means two real roots, zero means one real root, negative means complex roots.

About this Calculator

Free online quadratic equation calculator. Solve quadratic equations, find roots, vertex, and discriminant. Step-by-step solutions with detailed explanations.

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