Which of the following quadratic equations has the solution set (1/2, 5)? Select all that apply
(x + 1/2)(x - 5) = 0
(x - 5)(2x - 1) = 0
(x + 5)(2x - 1) = 0
(-2x + 1)(-x + 5) = 0
(x + 1/2)(x + 5) = 0
(-2x + 1)(x - 5) = 0

Solution:

The quadratic equations which have the solution as (1/2, 5) are determined are shown below:

(x - 5)(2x - 1) = 0

The two zeros of the quadratic equation are:

x - 5 = 0 ⇒ x = 5

(2x -1) = 0 ⇒ 2x = 1 ⇒ x = 1/2

(-2x + 1)(-x + 5) = 0

The two zeroes of the quadratic equation are:

-2x + 1 = 0 ⇒ 1 = 2x ⇒ x = 1/2

-x + 5 = 0 ⇒ 5 = x

Hence (-2x + 1)(-x + 5) = 0 is another equation which gives the desired solution of (1/2, 5)

(-2x + 1)(x - 5) = 0

The two zeros of the quadratic polynomial are

-2x + 1 = 0 ⇒ 1 = 0 + 2x ⇒ 1/2 = x

x - 5 = 0 ⇒ x = 5

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Which of the following quadratic equations has the solution set (1/2, 5)? Select all that apply

Summary:

The quadratic equations that have the solution set (1/2, 5) are (x - 5)(2x - 1) = 0, (-2x + 1)(-x + 5) = 0 and (-2x + 1)(x - 5) = 0