Question

The discriminant of the quadratic equation \(3x^2 - 2x + \frac{1}{3} = 0\) is:

• A. 32
• B. 16
• C. 0
• D. 1

Hint:

The discriminant of a quadratic equation determines the nature of its roots: - If \(\Delta>0\), the roots are real and distinct. - If \(\Delta = 0\), the roots are real and equal. - If \(\Delta<0\), the roots are imaginary.

Answer 1

The Correct Option is B

For the quadratic equation \(ax^2 + bx + c = 0\), the discriminant \(\Delta\) is given by: \[ \Delta = b^2 - 4ac \] For the equation \(3x^2 - 2x + \frac{1}{3} = 0\), we have \(a = 3\), \(b = -2\), and \(c = \frac{1}{3}\). Substituting these values into the discriminant formula: \[ \Delta = (-2)^2 - 4(3)\left(\frac{1}{3}\right) \] \[ \Delta = 4 - 4 = 0 \] Thus, the discriminant is 0. Therefore, the correct answer is option (3).