Find all the real zeros of the polynomial function. $f ( x ) = x ^ { 5 } - 16 x ^ { 3 } + 64 x$
A) $0 , \pm \sqrt { 8 }$
B) $0 , \sqrt { 8 }$
C) 0,8
D) $0 , - 8$
E) $0 , - \sqrt { 8 }$

Question

Find all the real zeros of the polynomial function. $f ( x ) = x ^ { 5 } - 16 x ^ { 3 } + 64 x$ 
A) $0 , \pm \sqrt { 8 }$
B) $0 , \sqrt { 8 }$
C) 0,8
D) $0 , - 8$
E) $0 , - \sqrt { 8 }$

Quizplus · Accepted Answer

We can factor out $x$ to get $x(x^4-16x^2+64)$. Then, factor the quadratic in the parentheses to get $x(x^2-8)^2$. Setting this equal to zero, we find the real zeros to be $0, \pm\sqrt{8}$. Therefore, the answer is $\boxed{	extbf{(A) }0 , \pm \sqrt { 8 }}$.

Find All the Real Zeros of the Polynomial Function f(x)=x5−16x3+64xf ( x ) = x ^ { 5 } - 16 x ^ { 3 } + 64 xf(x)=x5−16x3+64x

Find All the Real Zeros of the Polynomial Function $f ( x ) = x ^ { 5 } - 16 x ^ { 3 } + 64 x$