Find all zeros of the function $f ( x ) = ( x + 6 ) ( x + 3 i ) ( x - 3 i )$.
A) $x = 6 , - 3 i , 3 i$
B) $x = - 6,3 i$
C) $x = - 6 , - 3,3$
D) $x = - 6 , - 3 i , 3 i$
E) $x = - 6$

Question

Quizplus · Accepted Answer

To find the zeros of the function, we set $f(x)=0$ and solve for $x$. Using the zero product property, we have $(x+6)(x+3i)(x-3i)=0$. This equation is true if and only if one (or more) of the factors is equal to zero. Therefore, we must solve the equations $x+6=0$, $x+3i=0$, and $x-3i=0$. Solving these equations gives $x=-6$, $x=-3i$, and $x=3i$. Thus, the zeros of the function are $x=-6$, $x=-3i$, and $x=3i$, which is only listed in choice D.

Find All Zeros of the Function f(x)=(x+6)(x+3i)(x−3i)f ( x ) = ( x + 6 ) ( x + 3 i ) ( x - 3 i )f(x)=(x+6)(x+3i)(x−3i)

Find All Zeros of the Function $f ( x ) = ( x + 6 ) ( x + 3 i ) ( x - 3 i )$