What is the quadratic formula?

The quadratic formula is derived from the standard form of a quadratic equation, which is expressed as (ax^2 + bx + c = 0). To find the solutions for (x), the quadratic formula provides a method for solving these equations in a systematic way.

The correct form is given as (x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}). Here, (b) represents the coefficient of the linear term, (a) is the coefficient of the quadratic term, and (c) is the constant term. The part under the square root, known as the discriminant ((b^2 - 4ac)), determines the nature of the roots. If the discriminant is positive, there are two distinct real roots. If it is zero, there is exactly one real root (a repeated root). If it is negative, there are two complex roots.

This formula allows for the straightforward computation of the values of (x) that satisfy the equation, regardless of the specific values of (a), (b), and (c) (as long as (a) is not zero, as it then would not be