The quadratic equation 3x² - 4√3 x + 4 = 0 has:

Correct option is D

Given:

​$$3x^2 - 4\sqrt{3}x + 4 = 0$$​​

Concept Used:

Nature of roots of a quadratic equation is determined using the discriminant D

D > 0: Two distinct real roots

D = 0: Two equal real roots

D < 0: Complex (non-real) roots

Formula Used:

​$$D = b^2 - 4ac$$​​

Solution:

​$$a = 3, b = -4\sqrt{3}, c = 4$$​​

D = $$(-4\sqrt{3})^2 - 4 \times 3 \times 4 = 48 - 48 = 0$$​

Since D = 0, the equation has two equal real roots.