Algebra-1

To find a function that has roots at -3, 1, and 4, we need to check each of the given options by substituting these values into the function and verifying if they result in f(x) equal to zero.

Option A:
f(x)= (x - 3) (x - 1) (x + 4)
When we substitute x = -3, we get: f(-3) = (-3 - 3)(-3 - 1)(-3 + 4) = -6 * -4 * 1 = -24.
When we substitute x = 1, we get: f(1) = (1 - 3)(1 - 1)(1 + 4) = -2 * 0 * 5 = 0.
When we substitute x = 4, we get: f(4) = (4 - 3)(4 - 1)(4 + 4) = 1 * 3 * 8= 24.
Option A does not satisfy the condition, as f(-3) ≠ 0 and f(4) ≠ 0. Therefore, it does not have the roots at -3, 1, and 4.

Option B:
f(x)= (x - 3) (x + 1) (x + 4)
When we substitute x = -3, we get: f(-3) = (-3 - 3)(-3 + 1)(-3 + 4) = -6 * -2 * 1 = -12.
When we substitute x = 1, we get: f(1) = (1 - 3)(1 + 1)(1 + 4) = -2 * 2 * 5 = -20.
When we substitute x = 4, we get: f(4) = (4 - 3)(4 + 1)(4 + 4) = 1 * 5 * 8= 40.
Option B does not satisfy the condition.

Option C:
f(x)= (x + 3) (x - 1) (x - 4)

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