Question

The discriminant of the equation $3x^2 - 2x + \frac{1}{3} = 0$, will be:

• A. 3
• B. 2
• C. 1
• D. 0

Hint:

The discriminant helps determine the nature of the roots of a quadratic equation. If $\Delta > 0$, there are two real roots; if $\Delta = 0$, there is one real root; if $\Delta < 0$, there are no real roots.

Answer 1

The Correct Option is C

The discriminant $\Delta$ of a quadratic equation $ax^2 + bx + c = 0$ is given by the formula: \[ \Delta = b^2 - 4ac \] For the equation $3x^2 - 2x + \frac{1}{3} = 0$, we identify the coefficients: \[ a = 3, \quad b = -2, \quad c = \frac{1}{3} \] Now, calculate the discriminant: \[ \Delta = (-2)^2 - 4 \times 3 \times \frac{1}{3} \] \[ \Delta = 4 - 4 = 0 \]
Step 2: Conclusion.
Therefore, the discriminant of the equation is $0$, so the correct answer is (D).