Question

Write a possible function in standard form given the zeros of 4, 3i, and -3i.

A. 10x^3 - 36x^2 - 36x + 144 = 0
B. 10x^3 - 27x^2 + 9x - 81 = 0
C. 10x^3 - 18x^2 - 18x + 64 = 0
D. 10x^3 - 27x^2 - 9x + 81 = 0

Answer 1

The function in standard form given the zeros 4, 3i, and -3i is 10x^3 - 36x^2 - 36x + 144 = 0.

Step-by-step explanation:

The given zeros of the function are 4, 3i, and -3i.

To find the function in standard form, we need to know that complex zeros occur in conjugate pairs. This means that if 3i is a zero, then -3i is also a zero.

Using the zero product property, we can write the factors of the function as (x - 4)(x - 3i)(x + 3i).

Expanding this expression, we obtain:
(x - 4)(x - 3i)(x + 3i) = (x - 4)(x^2 - 9i^2) = (x - 4)(x^2 + 9) = x^3 + 9x - 4x^2 - 36 = x^3 - 4x^2 + 9x - 36

Therefore, the correct option is A: 10x^3 - 36x^2 - 36x + 144 = 0.