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) $\quad x = 0,2,6 , - 3 - 3 \sqrt { 3 } i , - 3 + 3 \sqrt { 3 } i$
D) $\quad x = - 2 , - 216$
E) $\quad x = 0,2,6$

Question

Quizplus · Accepted Answer

The zeros of the function can be found by setting each factor equal to zero: $x^2 = 0$ gives $x = 0$, $x - 2 = 0$ gives $x = 2$, and $x^3 - 216 = 0$ gives $x^3 = 216$, which results in $x = 6$ for the real root. The cubic equation also has two complex roots, which are $-3 - 3\sqrt{3}i$ and $-3 + 3\sqrt{3}i$.

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 $f ( x ) = x ^ { 2 } ( x - 2 ) \left( x ^ { 3 } - 216 \right)$