Use the discriminant, $LaTeX: \displaystyle b^2-4ac$ to determine the number and type of solutions to the equation $LaTeX: \displaystyle - x^{2} + 4 x - 8 = 0$ . No points will be given if the discriminant is not used.

Since the discriminant is $LaTeX: \displaystyle b^2-4ac=(4)^2-4(-1)(-8)=-16$ and is negative, the equation has two imaginary solutions.