Find the discriminant of the quadratic equation $3x^2 -2x + \frac{1}{3} = 0$ and hence find the nature of its roots

Find the discriminant of the quadratic equation $ 3x^2 - 2x + \frac{1}{3} = 0 $ and  hence find the nature of its roots

Answer

$$ 3x^2 -2x + \frac{1}{3} = 0 $$

$$ a = 3, b = -2, c = \frac{1}{3} $$

$$ D = b^2 - 4ac = (-2)^2 - 4(3)\left(\frac{1}{3}\right) = 0 $$

Roots are real and equal.