Using a graphing utility,graph $f ( x ) = x ^ { 3 } - 4 x$ and approximate the zeros and their multiplicity.
A) $x = 0 , \text { multiplicity } 2 ; x = - 2 \text {, multiplicity } 1$
B) $x = 0 \text {, multiplicity } 1 ; x = 2 \text {, multiplicity } 1 ; x = - 2 \text {, multiplicity } 1$
C) $x = 0 , \text { multiplicity } 3$
D) $x = 0 , \text { multiplicity } 1 ; x = 2 , \text { multiplicity } 2$
E) $x = 2 , \text { multiplicity } 2 ; x = - 2 \text {, multiplicity } 1$

Question

Quizplus · Accepted Answer

The zeros of the function $f(x) = x^3 - 4x$ can be found by setting the function equal to zero and solving for $x$. This gives $x^3 - 4x = 0$, which factors to $x(x^2 - 4) = 0$, further factoring to $x(x - 2)(x + 2) = 0$. This results in zeros at $x = 0$, $x = 2$, and $x = -2$, each with a multiplicity of 1, as each factor is to the first power.

Using a Graphing Utility,graph f(x)=x3−4xf ( x ) = x ^ { 3 } - 4 xf(x)=x3−4x

Using a Graphing Utility,graph $f ( x ) = x ^ { 3 } - 4 x$