Discuss the nature of the roots of the following equation without actually solving it:

2x² + 2x + 3 = 0

Comparing 2x² + 2x + 3 = 0 with ax² + bx + c = 0 we get,

a = 2, b = 2 and c = 3.

We know that,

Discriminant (D) = b² - 4ac = (2)² - 4 × 2 × 3

= 4 - 24 = -20; which is negative.

Hence, the roots are imaginary and unequal.