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

x² + $2\sqrt{3}x$ - 1 = 0

Comparing x² + $2\sqrt{3}x$ - 1 = 0 with ax² + bx + c = 0 we get,

a = 1, b = $2\sqrt{3}$ and c = -1.

We know that,

Discriminant = D = b² - 4ac = $(2\sqrt{3})^2$ - 4 × 1 × -1

= (2 × 3) + 4 = 10 ; which is positive and is not a perfect square.

Since, b is irrational and discriminant is greater than zero.

Hence, the roots are irrational and unequal.