Answer
\begin{align*}
\text{Discriminant: }&
-4
\\\text{Number of Real Solutions: }&
0
\end{align*}
Work Step by Step
In the given equation,
\begin{align*}
x^2+4x+5=0
,\end{align*} $a=
1
,$ $b=
4
,$ 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}
&
4^2-4(1)(5)
\\&=
16-20
\\&=
-4
\end{array}
Since the discriminant is less than $0,$ then there are no real solutions. Hence,
\begin{align*}
\text{Discriminant: }&
-4
\\\text{# of Real Solutions: }&
0
\end{align*}
