What is the correct form of the Quadratic Formula?

The correct form of the Quadratic Formula is derived from the standard form of a quadratic equation, which is expressed as ( ax^2 + bx + c = 0 ). To solve for ( x ), we use the quadratic formula:

[

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

]

This formula allows us to find the roots (or solutions) of any quadratic equation.

The part of the formula 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, and if it is negative, there are two complex roots.

The correct option states ( x = -b \pm \sqrt{b^2 - 4ac} ), clearly indicating the use of the negative sign in front of ( b ) and the proper sign of the discriminant. Additionally, it ensures that everything is divided by ( 2a ), which is crucial for obtaining proper solutions.

In contrast, the other options contain errors such as incorrect signs for ( b