Question

If f(x) = x³ - 13x² + 39x - 27 and f(-3) = 0, find all of the zeros of f(x).

a) x = -1, x = 3
b) x = -3, x = 1
c) x = -9, x = 3
d) x = -3, x = 9

Answer 1

To find all the zeros of the polynomial function f(x), factor the polynomial using the given zero x = -3, then use the quadratic formula on the resulting quadratic equation to find the remaining zeros.

Step-by-step explanation:

The student has asked how to find all the zeros of the polynomial function f(x) = x³ - 13x² + 39x - 27, given that f(-3) = 0. To find the remaining zeros, we use the fact that (-3) is a zero to factor the polynomial and then apply the quadratic formula to find the other zeros.

We can factor by long division or synthetic division since we already know one zero, which is -3. After factoring, we will have a quadratic equation for which we apply the quadratic formula: -b ± √(b² - 4ac) / (2a). Once we calculate the discriminant and find the square root, we divide by 2a to find the other two zeros of the polynomial.

Based on the information provided and the lack of specific calculation details, it is not possible to definitely conclude the correct option without additional working out of the problem. However, it seems that there might be some information missing to accurately complete the solution.