Use the discriminant, $LaTeX: \displaystyle b^2-4ac$ to determine the number and type of solutions to the equation $LaTeX: \displaystyle 10 x^{2} + 3 x + 1 = 0$ . No points will be given if the discriminant is not used.

Since the discriminant is $LaTeX: \displaystyle b^2-4ac=(3)^2-4(10)(1)=-31$ and is negative, the equation has two imaginary solutions.