What is the quadratic formula?

The quadratic formula is used to find the solutions (or roots) of a quadratic equation, which is typically expressed in the standard form ax² + bx + c = 0, where a, b, and c are constants. The correct expression for the quadratic formula is derived from completing the square of a quadratic equation.

The formula is given as:

x = (-b ± √(b² - 4ac)) / (2a)

This formula correctly utilizes the discriminant, expressed as b² - 4ac, which determines the nature and number of the roots. Specifically, if the discriminant is positive, there are two distinct real roots; if it is zero, there is one real root (or a repeated root); and if it is negative, the roots are complex.

In the correct answer, the square root part, √(b² - 4ac), accurately reflects how the solutions are determined based on the discriminant. The ± symbol indicates that there are generally two solutions to the quadratic equation. Dividing by 2a is essential for scaling the result appropriately based on the coefficient a of the x² term.

The other choices include variations of the formula that either alter the discriminant or misrepresent the relationship in