The nature of the roots of x^2 + 3x + 6 = 0 is complex (imaginary) roots.

Examine the discriminant (b^2 - 4ac) of the equation.

In this case, a = 1, b = 3, and c = 6.

The discriminant is calculated as follows:

Discriminant = (3^2) - 4(1)(6)
= 9 - 24
= -15

Since the discriminant (-15) is negative, the quadratic equation has complex roots. Specifically, it has two imaginary roots, indicating that the equation does not intersect the x-axis and has no real solutions.

Therefore, the nature of the roots of x^2 + 3x + 6 = 0 is complex (imaginary) roots.