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

Answer:

Option d) is correct

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

Step-by-step 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

$x=\frac{-11}{2}$    or   $2x=11$

$x=\frac{-11}{2}$    or   $x=\frac{11}{2}$

$x=\pm \frac{11}{2}$

Therefore option d) is correct

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