Answer
Zeros: $0,16$
$x$-intercepts: $0,16$
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 $G(x)=0$:
$$x-4\sqrt{x}=0$$
Let $u=\sqrt{x}$, the original equation becomes
$$u^2-4u=0$$
By factoring
$$u(u-4) = 0$$
Use the Zero-Product Property by equating each factor to zero, then solve each equation to obtain:
\begin{align*}
u &= 0 &\text{ or }& &u-4=0\\
u &= 0 &\text{ or }& &u=4\\
\end{align*}
To solve for $x$, we use $u=\sqrt{x}$
$$\because u=\sqrt{x}$$
$$\therefore x =u^2$$
For $u=0$
$$x=(0)^2 $$
$$x= 0$$
For $u=4$
$$x=(4)^2$$
$$x= 16$$
$\therefore x =0,16$
