Which formula is commonly used to find the solutions of a quadratic equation?

The Quadratic Formula is a specific mathematical tool used to solve quadratic equations, which are equations of the form ( ax^2 + bx + c = 0 ), where ( a ), ( b ), and ( c ) are constants, and ( a \neq 0 ). The Quadratic Formula states that the solutions for ( x ) can be found using the formula:

[

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

]

This formula provides the roots of the equation directly, allowing you to find the values of ( x ) that satisfy the equation. It addresses both real and complex solutions, as the term under the square root (the discriminant, ( b^2 - 4ac )) determines the nature of the roots. If the discriminant is positive, there are two distinct real solutions; if it is zero, there is one repeated real solution; and if it is negative, there are two complex solutions.

In contrast, the other options relate to different aspects of quadratic equations or other types of equations. The Square Root Formula, while useful, only applies in specific cases and is not appropriate for all quadratic equations. The