The given quadratic equation 3x 2 + $\sqrt{7}$ x + 2 = 0 has:

Comparing the given quadratic equation with ax² + bx + c = 0, we get :

a = 3, b = $\sqrt{7}$ and c = 2

Discriminant = b² - 4ac

= $(\sqrt{7})^2$ - 4 x 3 x 2

= 7 - 24

= -17.

Since, D < 0, there are no real roots.

Hence, option 4 is the correct option.