Find all the zeros (real and complex)of the function.
-$f ( x ) = x ^ { 4 } - 12 x ^ { 2 } - 64$
A) $- 2 \mathrm { i } , 2 \mathrm { i } , 8 \mathrm { i } , - 8 \mathrm { i }$
B) $- 2 \mathrm { i } , 2 \mathrm { i } , 4 , - 4$
C) $- 2 \mathrm { i } , 2 \mathrm { i } , 4 \mathrm { i } , - 4 \mathrm { i }$
D) $- 2 \mathrm { i } , 2 \mathrm { i } , 8 , - 8$

Question

Quizplus · Accepted Answer

To find the zeros of $f(x) = x^4 - 12x^2 - 64$, we can treat it as a quadratic in form by substituting $y = x^2$, giving us $y^2 - 12y - 64 = 0$. Solving this quadratic equation yields $y = 4$ and $y = -16$. Substituting back $x^2 = y$, for $y = 4$, we get $x = \pm 2$, and for $y = -16$, we get $x = \pm 4i$. Therefore, the zeros are $-2i, 2i, 4, -4$.

Find All the Zeros (Real and Complex)of the Function f(x)=x4−12x2−64f ( x ) = x ^ { 4 } - 12 x ^ { 2 } - 64f(x)=x4−12x2−64

Find All the Zeros (Real and Complex)of the Function $f ( x ) = x ^ { 4 } - 12 x ^ { 2 } - 64$