Chapter 4 Quadratic Functions and Factoring - 4.8 Use the Quadratic Formula and the Discriminant - 4.8 Exercises - Skill Practice - Page 296: 33

Two imaginary solutions

We first check that the function is in the form $ax^2+bx+c$. 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: $$8^2-4(8)(3)=-32$$ Thus, there are two imaginary solutions.