Question

If f(x) = x3 - 12x2 + 39x - 28 and f(1) = 0, then find all of the zeros of f (x) algebraically.

a) x = 1 , x = 4, x = 7
b) x = 1 , x = 2 , x = 14
c) x = 2 , x = 3 , x = 7
d) x = 4 , x = 7 , x = 14

Answer 1

To find the zeros of the function f(x) = x³ - 12x² + 39x - 28, we use polynomial division or factoring. The zeros of the function are x = 1, x = 4, and x = 7.

Step-by-step explanation:

To find the zeros of the function f(x) = x³ - 12x² + 39x - 28, we need to solve the equation f(x) = 0. Since we are given that f(1) = 0, we know that x = 1 is one of the solutions. To find the other solutions, we can use polynomial division or factoring.

Performing synthetic division or factoring the polynomial, we find that f(x) can be factored as (x-1)(x-4)(x-7). Therefore, the zeros of f(x) are x = 1, x = 4, and x = 7.