Find all complex zeros of the polynomial function. Give exact values. List multiple zeros as necessary.
-$$f ( x ) = x ^ { 3 } - 3 x ^ { 2 } - 5 x + 39$$
A) $- 3,3 + 2 i , 3 - 2 i$
B) $- 3,3 + 4 i , 3 - 4 i$
C) $- 3,1 + 2 i , 1 - 2 i$
D) $- 3,1 + 2 \sqrt { 13 } i , 1 - 2 \sqrt { 13 } i$

Question

Quizplus · Accepted Answer

The polynomial can be factored or solved using techniques such as synthetic division or the Rational Root Theorem to find one real root, which is $x = -3$. The remaining roots can be found using the quadratic formula or further factoring, leading to the complex roots $3 + 2i$ and $3 - 2i$, making option A correct.

Find All Complex Zeros of the Polynomial Function f(x)=x3−3x2−5x+39f ( x ) = x ^ { 3 } - 3 x ^ { 2 } - 5 x + 39f(x)=x3−3x2−5x+39

Find All Complex Zeros of the Polynomial Function $f ( x ) = x ^ { 3 } - 3 x ^ { 2 } - 5 x + 39$