Question

Which equations have the solution set of {14, −5}
?

Select all that apply.

(3 points)
Responses

(8x - 2)(x + 5) = 0
(8x - 2)(x + 5) = 0

(x + 14)(x + 5) = 0
(x + 14)(x + 5) = 0

(x − 14)(x − 5) = 0
(x − 14)(x − 5) = 0

(2x - 8)(x - 5) = 0
(2x - 8)(x - 5) = 0

(4x − 1)(x+5)=0
(4x − 1)(x+5)=0

(x − 14)(x + 5) = 0
(x − 14)(x + 5) = 0

(4x + 2)(x + 5) = 0

Answer 1

To determine which equations have the solution set {14, -5}, we analyze each provided equation to see what values of \( x \) would satisfy them.

1. **(8x - 2)(x + 5) = 0**
- Solutions: \( 8x - 2 = 0 \) gives \( x = \frac{2}{8} = \frac{1}{4} \).
- \( x + 5 = 0 \) gives \( x = -5 \).
- Solutions are {−5, 0.25}, so this equation does not work.

2. **(x + 14)(x + 5) = 0**
- Solutions: \( x + 14 = 0 \) gives \( x = -14 \).
- \( x + 5 = 0 \) gives \( x = -5 \).
- Solutions are {−14, −5}, so this equation does not work.

3. **(x − 14)(x − 5) = 0**
- Solutions: \( x - 14 = 0 \) gives \( x = 14 \).
- \( x - 5 = 0 \) gives \( x = 5 \).
- Solutions are {14, 5}, so this equation does not work.

4. **(2x - 8)(x - 5) = 0**
- Solutions: \( 2x - 8 = 0 \) gives \( x = 4 \).
- \( x - 5 = 0 \) gives \( x = 5 \).
- Solutions are {4, 5}, so this equation does not work.

5. **(4x − 1)(x + 5) = 0**
- Solutions: \( 4x - 1 = 0 \) gives \( x = \frac{1}{4} \).
- \( x + 5 = 0 \) gives \( x = -5 \).
- Solutions are {−5, 0.25}, so this equation does not work.

6. **(x − 14)(x + 5) = 0**
- Solutions: \( x - 14 = 0 \) gives \( x = 14 \).
- \( x + 5 = 0 \) gives \( x = -5 \).
- Solutions are {14, -5}, so this equation works.

7. **(4x + 2)(x + 5) = 0**
- Solutions: \( 4x + 2 = 0 \) gives \( x = -\frac{1}{2} \).
- \( x + 5 = 0 \) gives \( x = -5 \).
- Solutions are {−5, -0.5}, so this equation does not work.

Based on this analysis, the equation that satisfies the solution set {14, −5} is:

- **(x − 14)(x + 5) = 0**

This is the only response that applies.