Multiple choice

Find the discriminant of the equation and the nature of roots. Also find the roots , if they are real: $3x^2 - 2x + \frac{1}{3} = 0$

  1. Roots are imaginary
  2. D $=$ 0, Roots are real and equal $\displaystyle \dfrac{1}{3}, \frac{1}{3}$
  3. D$ =$ $\dfrac{2}{5}$, Roots are real and unequal $\displaystyle \frac{1}{5}, \frac{1}{2}$

  4. Cannot be determined
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Equation: 3x^2 - 2x + 1/3 = 0. Multiply by 3: 9x^2 - 6x + 1 = 0. This is (3x-1)^2 = 0. Discriminant D = (-6)^2 - 4*9*1 = 36 - 36 = 0. Roots are 1/3, 1/3.

AI explanation

To clear the fraction, multiply the entire equation by 3 to get 9x squared minus 6x plus 1 equals 0. Using the discriminant formula, D equals b squared minus 4ac, we substitute a equals 9, b equals negative 6, and c equals 1. This results in D equals 36 minus 36, which equals 0, indicating real and equal roots. Using the quadratic formula, x equals 6 divided by 18, simplifying to one third for both roots.

Keep practicing — related questions