Question

Solve the quadratic equation 4x2 − 121 = 0. Verify your answer using a difference-of-squares factoring method.

a, x equals plus or minus start fraction two over 11 end fraction

b. x equals start fraction two over 11 end fraction

c. x equals start fraction 11 over two end fraction

d. x equals plus or minus start fraction 11 over two end fraction

Answer 1

Option d) is correct

That is x equals plus or minus start fraction 11 over two end fraction

Explanation:

Given quadratic equation is
`4x^2-121=0`

To write the given quadratic equation by using a difference-of-squares factoring method:

`4x^2-121=0`

The above equation can be written as

`4x^2-11^2=0`

`(2x)^2-11^2=0`

The above equation is in the form of difference-of-squares

Therefore the given quadratic equation can be written in the form of difference-of-squares

by factoring method is
`(2x)^2-11^2=0`

`(2x+11)(2x-11)=0` (which is in the form
`a^2-b^2=(a+b)(a-b)` )

2x+11=0 or 2x-11=0

`x=(-11)/(2)` or
`2x=11`

`x=(-11)/(2)` or
`x=(11)/(2)`

`x=\pm (11)/(2)`

Therefore option d) is correct

That is x equals plus or minus start fraction 11 over two end fraction