Answer
discriminant: 17
number of solution: Choice C
Work Step by Step
The given equation, $
x^2+5x+2=0
,$ has
\begin{align*}a=
1
,b=
5
,\text{ and }c=
2
.\end{align*}
Using $
b^2-4ac
$ or the discriminant, then
\begin{align*}
b^2-4ac&\Rightarrow
5^2-4(1)(2)
\\&=
25-8
\\&=
17
.\end{align*}
Since the discriminant is $
17
$ (which is positive and a non-perfect square), then the solutions of the given equation are two irrational numbers (Choice C).
