Which formula is used to solve quadratic equations?

The formula used to solve quadratic equations is derived from the quadratic formula, which is explicitly written as x = (-b ± √(b² - 4ac)) / 2a. This formula applies to equations of the form ax² + bx + c = 0, where a, b, and c are constants, and a is not equal to zero.

In this formula, -b represents the negation of the linear coefficient, and the term √(b² - 4ac) is known as the discriminant, which indicates the nature of the roots of the quadratic equation. If the discriminant is positive, there are two distinct real roots; if it is zero, there is one real root (a repeated root); and if it is negative, the roots are complex. The division by 2a adjusts the results according to the coefficient of x² in the original equation.

The other formulas presented do not correctly represent the standard quadratic formula. The second option mistakenly adds the term under the square root, which should be a subtraction related to the nature of the roots. The third option alters the structure entirely, leading to an incorrect representation. The last option changes the square root calculation incorrectly and disregards the necessary negative sign