Answer: Yes, the equation has two imaginary solutions
Explanation
That equation is of the template [tex]a \text{x}^2 + b \text{x} + c = 0[/tex] where,
Let's plug those values into the discriminant formula.
[tex]d = b^2 - 4ac\\\\d = (-4)^2 - 4(1)(13)\\\\d = 16 - 52\\\\d = -36\\\\[/tex]
The discriminant is negative which leads to two imaginary solutions. This is because we have a negative number under the square root in the quadratic formula.
The two imaginary solutions are x = 2+3i and x = 2-3i where [tex]i = \sqrt{-1}[/tex]
