Answer
Zero:$1$
$x$-intercept: $1$
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 $f(x)=0$:
$$x+\sqrt{x}-2=0$$
Let $u=\sqrt{x}$, the original equation becomes
$$u^2+u-2=0$$
By factoring
$$(u+2)(u-1) = 0$$
Use the Zero-Product Property by equating each factor to zero, then solve each equatin to obtain:
\begin{align*}
u +2&=0 &\text{ or }& &u-1=0\\
u &= -2 &\text{ or }& &u=1\\
\end{align*}
To solve for $x$, we use $u=\sqrt{x}$
For $u=-2$
$$\sqrt{x}=-2 \hspace{5pt} \to \hspace{5pt} \text{No Solution}$$
For $u=1$
$$\sqrt{x}=1$$
$$\therefore x = 1$$
$\therefore x =1$
