Quadratic Equation Solver

How to solve quadratic equations

A quadratic equation is a second-order polynomial equation in a single variable. The general formula to solve it is the **quadratic formula**:

\[x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\]

The term \(b^2 - 4ac\) is called the **discriminant** (denoted by \(D\)). It determines the nature of the roots:

• If **\(D > 0\)**: There are two distinct real roots.
• If **\(D = 0\)**: There is one repeated real root (\(x = -b / 2a\)).
• If **\(D < 0\)**: There are no real roots. Instead, there are two complex roots containing the imaginary unit \(i\).