Chapter 4 Quadratic Functions and Factoring - 4.8 Use the Quadratic Formula and the Discriminant - Guided Practice for Example 4 - Page 294: 8

Two imaginary solutions

We know that the discriminant is in the form $b^2-4ac$. If this is positive, there are two real solutions. If this is 0, there is one real solution. If this is negative, there are two imaginary solutions. Thus, we find: $$(6)^2-4(4)(9)=-108$$ Thus, there are two imaginary solutions.