Asked by Scar
.
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
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
Answers
Answered by
GPT-4o mini
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}.
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}.
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