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
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Common Quadratic Equations
Understanding Quadratic Equations
The Quadratic Formula
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.