Question

.

Which equations have the solution set of {1/4, −5}
?

Select all that apply.

(3 points)
Responses

(4x − 1)(x+5)=0
(4x − 1)(x+5)=0

(x − 1/4)(x + 5) = 0
(x − 1/4)(x + 5) = 0

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

(x + 1/4)(x + 5) = 0
(x + 1/4)(x + 5) = 0

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

(x − 1/4)(x − 5) = 0
(x − 1/4)(x − 5) = 0

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

Answer 1

To determine which equations have the solution set of {1/4, −5}, we can set each equation equal to zero and find the solutions.

1. **(4x − 1)(x + 5) = 0**
- Set each factor to zero:
- \(4x - 1 = 0 \Rightarrow x = \frac{1}{4}\)
- \(x + 5 = 0 \Rightarrow x = -5\)
- **Solutions: {1/4, -5} (This equation is valid)**

2. **(x − 1/4)(x + 5) = 0**
- Set each factor to zero:
- \(x - \frac{1}{4} = 0 \Rightarrow x = \frac{1}{4}\)
- \(x + 5 = 0 \Rightarrow x = -5\)
- **Solutions: {1/4, -5} (This equation is valid)**

3. **(4x + 2)(x + 5) = 0**
- Set each factor to zero:
- \(4x + 2 = 0 \Rightarrow x = -\frac{1}{2}\)
- \(x + 5 = 0 \Rightarrow x = -5\)
- **Solutions: {-1/2, -5} (This equation is not valid)**

4. **(x + 1/4)(x + 5) = 0**
- Set each factor to zero:
- \(x + \frac{1}{4} = 0 \Rightarrow x = -\frac{1}{4}\)
- \(x + 5 = 0 \Rightarrow x = -5\)
- **Solutions: {-1/4, -5} (This equation is not valid)**

5. **(2x - 8)(x - 5) = 0**
- Set each factor to zero:
- \(2x - 8 = 0 \Rightarrow x = 4\)
- \(x - 5 = 0 \Rightarrow x = 5\)
- **Solutions: {4, 5} (This equation is not valid)**

6. **(x − 1/4)(x − 5) = 0**
- Set each factor to zero:
- \(x - \frac{1}{4} = 0 \Rightarrow x = \frac{1}{4}\)
- \(x - 5 = 0 \Rightarrow x = 5\)
- **Solutions: {1/4, 5} (This equation is not valid)**

7. **(8x - 2)(x + 5) = 0**
- Set each factor to zero:
- \(8x - 2 = 0 \Rightarrow x = \frac{1}{4}\)
- \(x + 5 = 0 \Rightarrow x = -5\)
- **Solutions: {1/4, -5} (This equation is valid)**

### Summary:
The equations that have the solution set of {1/4, −5} are:

1. **(4x − 1)(x + 5) = 0**
2. **(x − 1/4)(x + 5) = 0**
3. **(8x - 2)(x + 5) = 0**