Find the zeros of the function below algebraically, if any exist. $$f ( x ) = x ^ { 5 } - 5 x ^ { 3 } + 4 x$$
A) $- 4 , - 1,1,4$
B) $- 4 , - 2,2,4$
C) $- 2 , - 1,0,1,2$
D) $- 4 , - 2,0,2,4$
E) No zeros exist.

Question

Quizplus · Accepted Answer

To find the zeros of the function $f(x) = x^5 - 5x^3 + 4x$, factor out the common term $x$, resulting in $x(x^4 - 5x^2 + 4)$. Further factor the quadratic in $x^2$ to get $x(x^2 - 1)(x^2 - 4)$, which simplifies to $x(x - 1)(x + 1)(x - 2)(x + 2)$. The zeros are $x = 0, \pm1, \pm2$.

Find the Zeros of the Function Below Algebraically, If Any f(x)=x5−5x3+4xf ( x ) = x ^ { 5 } - 5 x ^ { 3 } + 4 xf(x)=x5−5x3+4x

Find the Zeros of the Function Below Algebraically, If Any $f ( x ) = x ^ { 5 } - 5 x ^ { 3 } + 4 x$