Question

Discriminant of the quadratic equation \( 3x^2 - 6x + 4 = 0 \) will be:

• A. 13
• B. 12
• C. \( 3\sqrt{6} \)
• D. -12

Hint:

The discriminant of a quadratic equation determines the nature of the roots. A negative discriminant indicates complex roots.

Answer 1

The Correct Option is B

Step 1: Use the formula for the discriminant.
The discriminant \( \Delta \) of a quadratic equation \( ax^2 + bx + c = 0 \) is given by: \[ \Delta = b^2 - 4ac \] For the quadratic equation \( 3x^2 - 6x + 4 = 0 \), we have \( a = 3 \), \( b = -6 \), and \( c = 4 \).
Step 2: Calculate the discriminant.
Substitute the values of \( a \), \( b \), and \( c \) into the discriminant formula: \[ \Delta = (-6)^2 - 4(3)(4) = 36 - 48 = -12 \]
Step 3: Conclusion.
Thus, the discriminant of the equation is \( -12 \), so the correct answer is (D) -12.