The nature of the roots of the equation, 3x² - $4\sqrt{3}x$ + 4 = 0 is:

1. real and equal

2. irrational and unequal

3. rational and unequal

4. imaginary and unequal

Comparing 3x² - $4\sqrt{3}x$ + 4 = 0 with ax² + bx + c = 0 we get,

a = 3, b = -$4\sqrt{3}$ and c = 4.

We know that,

⇒ D = b² - 4ac

⇒ D = (-$4\sqrt{3}$)² - 4(3)(4)

⇒ D = 16(3) - 48

⇒ D = 48 - 48

⇒ D = 0.

Thus, roots are real and equal.

Hence, option 1 is the correct option.