Answer
$2$ imaginary conjugate solutions
Work Step by Step
The equation is in the standard form.
To determine the number and the type of the solutions for the equation $ax^2+bx+c=0$, we have to calculate the discriminant $\Delta=b^2-4ac$ and compare it to zero.
Identify $a$, $b$, $c$:
$$\begin{align*}
a&=1\\
b&=-4\\
c&=13.
\end{align*}$$
Calculate the discriminant:
$$\begin{align*}
\Delta=(-4)^2-4(1)(13)=-36.
\end{align*}$$
Because $\Delta<0$, the equation has $2$ imaginary conjugate solutions.
