Answer
$\text{no $x$-intercept}$
Work Step by Step
Using $y=ax^2+bx+c,$ the given equation,
\begin{align*}
y=x^2+3x+5
,\end{align*} has $a=
1
,$ $b=
3
,$ and $c=
5
.$
Using the Discriminant Formula which is given by $b^2-4ac,$ the value of the discriminant is
\begin{array}{l}\require{cancel}
&
3^2-4(1)(5)
\\&=
9-20
\\&=
-11
\end{array}
Since the discriminant is less than $0,$ then there is no real solution. With no real solution, then there is $
\text{no $x$-intercept}
.$
