Question

What are the real and complex zeros of the function f(x) = x^3 - 2x^2 - 11x + 12?

A. x = 4, x = 3, x = -1
B. x = 3, x = -4, x = 1
C. x = 4, x = -1, x = -3
D. x = 1, x = -2, x = -6

Answer 1

The real zeros are x = 4, x = -1, and x = -3. The complex zeros are x = 4, x = -1, and x = -3.

Step-by-step explanation:

The function f(x) = x^3 - 2x^2 - 11x + 12 is a cubic function. To find the real and complex zeros of the function, we can use the Rational Zero Theorem and synthetic division.

By using synthetic division with possible rational zeros such as ±1, ±2, ±3, ±4, ±6, and ±12, we find that x = 4, x = -1, and x = -3 are the real zeros of the function. We can then factor the function as (x - 4)(x + 1)(x + 3) = 0 and solve for the complex zeros.

The complex zeros of the function f(x) = x^3 - 2x^2 - 11x + 12 are x = 4, x = -1, and x = -3.