Question

Give an example of a quadratic with complex roots. Explain how you know it has complex roots.

Answer 1

2x^2 + x + 3=0 has only complex roots.

The determinant is 1-4*2*3 = -23

-23 (or any determinant) is the part under the square root sign,  If that determinant is negative, knowing you cannot take the square root of a negative number, we know the answers must be complex.