Algebra-1

The correct answer is D. f(x) = (x + 2) (x - 5) (3x - 2) is the function that has roots at -2, 5, and 2/3.

To determine which of the given functions has roots at -2, 5, and 2/3, we need to substitute these values into each function and check if they result in f(x) being equal to zero.

Option A:
f(x) = (x - 2)(x + 5)(3x + 2)
When we substitute x = -2, we get: f(-2) = (-2 - 2)(-2 + 5)(3(-2) + 2) = -4 * 3 * -4 = 48.
When we substitute x = 5, we get: f(5) = (5 - 2)(5 + 5)(3(5) + 2) = 3 * 10 * 17 = 510.
When we substitute x = 2/3, we get: f(2/3) = (2/3 - 2)(2/3 + 5)(3(2/3) + 2) = -4/3 * 17/3 * 10/3 = -680/27.
Option A does not satisfy the condition, as f(-2), f(5), and f(2/3) are not equal to zero. Therefore, it does not have the roots at -2, 5, and 2/3.

Option B:
f(x) = (x - 2)(x + 5)(2x + 3)
When we substitute x = -2, we get: f(-2) = (-2 - 2)(-2 + 5)(2(-2) + 3) = -4 * 3 * -1 = 12.
When we substitute x = 5, we get: f(5) = (5 - 2)(5 + 5)(2(5) + 3) = 3 * 10 * 13 = 390.
When we substitute x = 2/3, we get: f(2/3) = (2/3 - 2)(2/3 + 5)(2(2/3) + 3) = -4/3 * 17/3 * 1...