What is a Quadratic Equation?

A quadratic equation is a second-order polynomial equation in a single variable x, typically expressed in the standard form: ax² + bx + c = 0. Here, x represents an unknown variable, while a, b, and c are constants (with a not equal to 0). Solving these equations is a fundamental skill in algebra, physics, and engineering.

How to Use This Calculator

Our calculator simplifies the process of finding roots by providing a detailed step-by-step breakdown. To use it, simply enter the numerical values for the coefficients 'a', 'b', and 'c' into the respective input fields and click "Calculate Roots." The tool instantly identifies whether the roots are real, equal, or complex.

The Quadratic Formula

The most common method for solving these equations is using the Quadratic Formula: x = [-b ± sqrt(b² - 4ac)] / 2a. The term inside the square root (b² - 4ac) is known as the Discriminant (D). The value of the discriminant determines the nature of the solutions:

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

Frequently Asked Questions

Can 'a' be zero? No, if 'a' is zero, the equation becomes linear (bx + c = 0), not quadratic.

What are imaginary roots? When the discriminant is negative, the square root results in an imaginary number (represented by 'i'), indicating that the parabola does not cross the x-axis.