Question

.

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

Select all that apply.

(3 points)
Responses

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

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

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

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

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

Answer 1

To determine which equations have the solution set {14, -5}, we need to check each equation and pinpoint its roots.

1. **(4x − 1)(x + 5) = 0**
- Roots:
- \(4x - 1 = 0 \Rightarrow x = \frac{1}{4}\)
- \(x + 5 = 0 \Rightarrow x = -5\)
- **Solutions**: {0.25, -5}

2. **(x − 14)(x + 5) = 0**
- Roots:
- \(x - 14 = 0 \Rightarrow x = 14\)
- \(x + 5 = 0 \Rightarrow x = -5\)
- **Solutions**: {14, -5}

3. **(4x + 2)(x + 5) = 0**
- Roots:
- \(4x + 2 = 0 \Rightarrow x = -\frac{1}{2}\)
- \(x + 5 = 0 \Rightarrow x = -5\)
- **Solutions**: {-0.5, -5}

4. **(x + 14)(x + 5) = 0**
- Roots:
- \(x + 14 = 0 \Rightarrow x = -14\)
- \(x + 5 = 0 \Rightarrow x = -5\)
- **Solutions**: {-14, -5}

5. **(2x - 8)(x - 5) = 0**
- Roots:
- \(2x - 8 = 0 \Rightarrow x = 4\)
- \(x - 5 = 0 \Rightarrow x = 5\)
- **Solutions**: {4, 5}

6. **(x − 14)(x − 5) = 0**
- Roots:
- \(x - 14 = 0 \Rightarrow x = 14\)
- \(x - 5 = 0 \Rightarrow x = 5\)
- **Solutions**: {14, 5}

7. **(8x - 2)(x + 5) = 0**
- Roots:
- \(8x - 2 = 0 \Rightarrow x = \frac{1}{4}\)
- \(x + 5 = 0 \Rightarrow x = -5\)
- **Solutions**: {0.25, -5}

### Conclusion:
The equations that have the solution set {14, -5} are:

- **(x − 14)(x + 5) = 0**

That’s the only valid equation from the list that provides the desired solution set {14, -5}.