Answer
Choice C;
should be solved using the Quadratic Formula
Work Step by Step
The discriminant of a quadratic equation $ax^2+bx+c=0,$ is given by $b^2-4ac$. Thus, the discriminant of the given equation, $
x^2+4x+2=0
,$ is
\begin{align*}\require{cancel}
&
4^2-4(1)(2)
\\&=
16-8
\\&=
8
.\end{align*}
Since the discriminant is positive and is a non-perfect square, then the equation $
x^2+4x+2=0
$ has two irrational numbers as solutions or $\text{
Choice C
}$.
Furthermore, since the discriminant is a non-perfect square, then the given equation CANNOT be solved using the Zero-Factor Property. Hence, the Quadratic Formula should be used.