what is quadratic formula equation

The quadratic formula is an equation that can be used to solve quadratic equations. A quadratic equation is an equation of the form ax² + bx + c = 0, where a, b, and c are real numbers and a ≠ 0. The quadratic formula is:

“`
x = (-b ± √(b² – 4ac)) / 2a
“`

To use the quadratic formula, you need to first identify the values of a, b, and c in the equation. Once you have identified these values, you can plug them into the formula to solve for x.

Here is an example of how to use the quadratic formula:

“`
Solve the equation x² + 2x – 3 = 0.

In this equation, a = 1, b = 2, and c = -3.

Plugging these values into the quadratic formula, we get:

x = (-2 ± √(2² – 4 × 1 × -3)) / 2 × 1

= (-2 ± √(4 + 12)) / 2

= (-2 ± √16) / 2

= (-2 ± 4) / 2

= (-2 + 4) / 2 or (-2 – 4) / 2

= 2 or -3

Therefore, the solutions to the equation x² + 2x – 3 = 0 are x = 2 and x = -3.
“`

The quadratic formula can be used to solve any quadratic equation. However, it is important to note that the quadratic formula may not always produce real solutions. If the discriminant, which is b² – 4ac, is negative, then the quadratic formula will produce two complex solutions.