What is the nature of the roots of the equation, 2x² - 6x + 3 = 0?

1. rational and unequal

2. irrational and unequal

3. real and equal

4. imaginary and unequal

Comparing 2x² - 6x + 3 = 0 with ax² + bx + c = 0 we get,

a = 2, b = -6 and c = 3.

We know that,

⇒ D = b² - 4ac

⇒ D = (-6)² - 4(2)(3)

⇒ D = 36 - 24

⇒ D = 12

⇒ D > 0 roots are real and unequal.

⇒ D = 12 is not a perfect square, roots are irrational.

Thus, roots are irrational and unequal.

Hence, option 2 is the correct option.