Answer
Zero/s: $0$
$x$-intercept: $0$
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 $f(x)=0$:
$$x+8\sqrt{x}=0$$
Let $u=\sqrt{x}$, the original equation becomes
$$u^2+8u=0$$
By factoring
$$u(u+8) = 0$$
Use the Zero-Product Property by equating rach factor to zero, then solve each equation to obtain:
\begin{align*}
u &= 0 &\text{ or }& &u+8=0\\
u &= 0 &\text{ or }& &u=-8\\
\end{align*}
To solve for $x$, we use $u=\sqrt{x}$
For $u=0$
$$\sqrt{x}=0$$
$$\therefore x = 0$$
For $u=-8$
$$\sqrt{x}=-8$$
$$\text{ No real solution}$$
$\therefore x =0$
