Answer
Zeros: $ 1,-1,2,-2 $
$x$-intercepts: $1,-1,2,-2 $
Work Step by Step
To find the zeros of a function $f$, solve the equation $f(x)=0$
The zeros of the function are also the $x-$intercepts.
Let $f(x)=0$:
$$x^4-5x^2+4=0$$
Let $u=x^2$, the original equation becomes
$$u^2-5u+4=0$$
By factoring
$$(u-1)(u-4) = 0$$
Use the Zero-Product Property by equating each factor to zero, then solve each equation to obtain:
\begin{align*}
u-1 &=0 &\text{ or }& &u-4=0\\
u &= 1 &\text{ or }& &u=4\\
\end{align*}
To solve for $x$, we use $u=x^2$
$$\because u = x^2$$
$$\therefore x = \pm \sqrt{u}$$
For $u=1$
$$x=\pm \sqrt{1} $$
$$x= \pm 1$$
For $u=4$
$$x= \pm \sqrt{4}$$
$$x= \pm 2$$
$\therefore x = 1,-1,2,-2 $
