Question

If roots of the equation \( 3x^2 - 12x + k = 0 \) are equal, then the value of \( k \) will be:

• A. 12
• B. 4
• C. 7
• D. 9

Hint:

For a quadratic equation to have equal roots, the discriminant must be zero. The discriminant is calculated as \( \Delta = b^2 - 4ac \).

Answer 1

The Correct Option is B

Step 1: Condition for equal roots.
For a quadratic equation \( ax^2 + bx + c = 0 \) to have equal roots, the discriminant must be zero. The discriminant \( \Delta \) is given by: \[ \Delta = b^2 - 4ac \] For the equation \( 3x^2 - 12x + k = 0 \), we have \( a = 3 \), \( b = -12 \), and \( c = k \).
Step 2: Apply the condition for equal roots.
For equal roots, \( \Delta = 0 \), so: \[ (-12)^2 - 4(3)(k) = 0 \] \[ 144 - 12k = 0 \]
Step 3: Solve for \( k \).
Solving for \( k \): \[ 12k = 144 \quad \Rightarrow \quad k = \frac{144}{12} = 12 \]
Step 4: Conclusion.
Thus, the value of \( k \) is \( 12 \). Therefore, the correct answer is (A) 12.