Answer
$\text{Discriminant: }
-3
\\\text{Number of real solutions: }
0$
Work Step by Step
Using $ax^2+bx+c=0,$ the given equation, \begin{align*}
x^2-5x+7=0
,\end{align*} has $a=
1
,$ $b=
-5
,$ and $c=
7
.$ Using $b^2-4ac$ or the Discriminant, then
\begin{align*}b^2-4ac&=
(-5)^2-4(1)(7)
\\&=
25-28
\\&=
-3
.\end{align*}
Since the discriminant above is less than $0,$ then there are no real solutions. Hence,
\begin{align*}
\text{Discriminant: }
-3
\\\text{Number of real solutions: }
0
.\end{align*}
