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# Factoring Using the Quadratic Formula

November 6, 2023 written by Rida Mirza

Quadratic formula is a useful tool that allows us to factor quadratic equations into the form

(x – a)(x – b). By factoring quadratics, we can find the solutions or roots of the equation.

## What is the Quadratic Formula?

The quadratic formula states that for a quadratic equation in the form

ax2 + bx + c = 0

the solutions are given by:

x = (-b ± √(b2 – 4ac)) / 2a

Where a, b, and c are the coefficients of the quadratic equation.

To use the formula, we first identify the values of a, b, and c from the given quadratic equation.

## Example of Factoring with the Quadratic Formula

Solve the equation x2 + 5x + 6 = 0 using the quadratic formula.

First, identify the coefficients ‘a,’ ‘b,’ and ‘c’ from your quadratic equation,

a = 1, b = 5, c = 6

Plugging into the formula:

x = (-5 ± √(25 – 4(1)(6))) / 2(1)

Simplifying:

x = (-5 ± √(25 – 24)) / 2

x = (-5 ± 1) / 2

Find the Roots:

x1 = (-5 + 1)/2 = -4/2 = – 2

x2 = -5-1/2 = -6/2 = -3

So, the roots of the quadratic equation are -2 and -3.

## FAQs

### What are the steps for factoring with the quadratic formula?

Identify a, b, and c from the quadratic equation ax2 + bx + c = 0
Plug a, b, and c into the formula: x = (-b ± √(b2 – 4ac)) / 2a
Simplify the formula with the given values
The resulting factors will be in the form (x – a)(x – b)

### When should you use the quadratic formula?

Use the quadratic formula when you need to factor a quadratic equation that cannot easily be factored otherwise. It provides a straightforward way to find the linear factors.

### What are some examples of when factoring quadratics is useful?

Finding the zeros, x-intercepts, or solutions of a quadratic
Rewriting a quadratic into vertex form
Graphing parabolas and analyzing their key features