Find all complex zeros of the polynomial function. Give exact values. List multiple zeros as necessary.
-$$f ( x ) = x ^ { 4 } - 36$$
A) $\sqrt { 6 } , - \sqrt { 6 }$
B) $\sqrt { 6 } , - \sqrt { 6 } i , \sqrt { 6 } i , - \sqrt { 6 }$
C) $\sqrt { 6 } , \sqrt { 6 } i$
D) $\sqrt { 6 } , - 6 i , 6 i , - \sqrt { 6 }$

Question

Quizplus · Accepted Answer

The polynomial $f(x) = x^4 - 36$ can be factored as $(x^2 - 6)(x^2 + 6)$, giving real roots $\sqrt{6}$ and $-\sqrt{6}$, and complex roots $\sqrt{6}i$ and $-\sqrt{6}i$.

Find All Complex Zeros of the Polynomial Function f(x)=x4−36f ( x ) = x ^ { 4 } - 36f(x)=x4−36

Find All Complex Zeros of the Polynomial Function $f ( x ) = x ^ { 4 } - 36$