Algebra-1

The correct answer is A. f(x) = x(x - 5)(x - 3) is the function that has roots at 0, 3, and 5.

To determine which of the given functions has roots at 0, 3, and 5, 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(x - 5)(x - 3)
When we substitute x = 0, we get: f(0) = 0(0 - 5)(0 - 3) = 0 * -5 * -3 = 0.
When we substitute x = 3, we get: f(3) = 3(3 - 5)(3 - 3) = 3 * -2 * 0 = 0.
When we substitute x = 5, we get: f(5) = 5(5 - 5)(5 - 3) = 5 * 0 * 2 = 0.
Option A satisfies the condition and has roots at 0, 3, and 5.

Option B:
f(x) = x(x + 5)(x - 3)
When we substitute x = 0, we get: f(0) = 0(0 + 5)(0 - 3) = 0 * 5 * -3 = 0.
When we substitute x = 3, we get: f(3) = 3(3 + 5)(3 - 3) = 3 * 8 * 0 = 0.
When we substitute x = 5, we get: f(5) = 5(5 + 5)(5 - 3) = 5 * 10 * 2 = 100.
Option B does not satisfy the condition, as f(5)...