Create a quadratic equation that has complex solutions

x^2 + x + 2 = 0.

Step-by-step explanation:

The discriminant b^2 - 4ac is < 0 for complex roots.

So we can choose appropriate values for a, b and c.

Let b = 1,  a = 1 and  c = 2 so b^2 - 4ac = 1 - 4*1*2 = -7.

So our equation is:

x^2 + x + 2 = 0.