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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

1 answer

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