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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}.