Find all zeros of the function $f ( x ) = x ^ { 2 } ( x - 2 ) \left( x ^ { 3 } - 216 \right)$.
A) $x = 2,216$
B) $ x = 0 , - 2 , - 6$
C) $ x = 0,2,6 , - 3 - 3 \sqrt { 3 } i , - 3 + 3 \sqrt { 3 } i$
D) $x = - 2 , - 216$
E) $ x = 0,2,6$

Question

Quizplus · Accepted Answer

The zeros of the function can be found by setting each factor equal to zero. For $x^2$, the zero is $x = 0$. For $x - 2$, the zero is $x = 2$. For $x^3 - 216$, we solve $x^3 = 216$, giving $x = 6$ as the real root, and two complex roots from the cubic equation, which are $x = -3 - 3\sqrt{3}i$ and $x = -3 + 3\sqrt{3}i$.

Find All Zeros of the Function f(x)=x2(x−2)(x3−216)f ( x ) = x ^ { 2 } ( x - 2 ) \left( x ^ { 3 } - 216 \right)f(x)=x2(x−2)(x3−216)

Find All Zeros of the Function $f ( x ) = x ^ { 2 } ( x - 2 ) \left( x ^ { 3 } - 216 \right)$