Find the real zeros of the function, state their multiplicities if it is a number other than 1.
-$f ( x ) = x ^ { 2 } \left( x ^ { 2 } - 4 \right) \left( x ^ { 2 } + 36 \right)$
A) $x = 0$, multiplicity: 2
$$x = 2 , x = - 2$$
B) $x = 0$, multiplicity: 2
$$\begin{array} { l }
x = 2 , x = - 2 \
x = 6 , x = - 6
\end{array}$$
C) $x = 0$, multiplicity: 2
$x = - 2$, multiplicity: 2
D) $\mathrm { x } = 0$, multiplicity: 2
$x = 2$, multiplicity: 2

Question

Find the real zeros of the function, state their multiplicities if it is a number other than 1.
-$f ( x ) = x ^ { 2 } \left( x ^ { 2 } - 4 \right) \left( x ^ { 2 } + 36 \right)$
A) $x = 0$, multiplicity: 2
$$x = 2 , x = - 2$$
B) $x = 0$, multiplicity: 2
$$\begin{array} { l } 
x = 2 , x = - 2 \
x = 6 , x = - 6
\end{array}$$
C) $x = 0$, multiplicity: 2
$x = - 2$, multiplicity: 2
D) $\mathrm { x } = 0$, multiplicity: 2
$x = 2$, multiplicity: 2

Quizplus · Accepted Answer

The function $f(x) = x^2(x^2 - 4)(x^2 + 36)$ has real zeros at $x = 0$, with a multiplicity of 2 (from $x^2$), and at $x = 2$ and $x = -2$ (from $x^2 - 4$). The term $x^2 + 36$ does not contribute any real zeros because it is always positive for all real $x$.

Find the Real Zeros of the Function, State Their Multiplicities f(x)=x2(x2−4)(x2+36)f ( x ) = x ^ { 2 } \left( x ^ { 2 } - 4 \right) \left( x ^ { 2 } + 36 \right)f(x)=x2(x2−4)(x2+36)

Find the Real Zeros of the Function, State Their Multiplicities $f ( x ) = x ^ { 2 } \left( x ^ { 2 } - 4 \right) \left( x ^ { 2 } + 36 \right)$