Quadratic Formula

The quadratic formula is a standard method for solving quadratic equations that can be written in the form ax² + bx + c = 0, where a is not zero. It provides the values of x that make the equation equal to zero.

Quadratic Formula

x = (−b ± √(b² − 4ac)) ÷ 2a

In this formula, a, b, and c are the coefficients from the quadratic equation. The plus-or-minus symbol means that there can be two solutions.

Using the Discriminant

The expression b² − 4ac is called the discriminant. If it is positive, the equation has two distinct real solutions. If it is zero, there is one repeated real solution. If it is negative, the solutions are complex numbers.

Example

For x² − 5x + 6 = 0, a = 1, b = −5, and c = 6. Substituting these values into the quadratic formula gives x = 2 or x = 3.

When to Use the Formula

The quadratic formula is especially useful when factoring is difficult or when a consistent algebraic method is preferred. Always write the equation in standard form before substituting the coefficients.