Quadratic Equation Solver

How to Solve Quadratic Equations?

A quadratic equation is a second-degree polynomial equation in a single variable x with the form:

ax² + bx + c = 0

The solutions (roots) of the equation can be found using the quadratic formula:

x = (-b ± √(b² - 4ac)) / (2a)

The discriminant (Δ = b² - 4ac) determines the nature of the roots:

• If Δ > 0: Two distinct real roots
• If Δ = 0: One repeated real root (two equal roots)
• If Δ < 0: Two complex conjugate roots

Applications of Quadratic Equations

Quadratic equations are used extensively in physics, engineering, economics, and many other fields to model various phenomena including projectile motion, area optimization problems, and electrical circuits.