Question

If the roots of the quadratic equation $3x^2 - 12x + m = 0$ are equal, then the value of $m$ will be:

• A. 4
• B. 7
• C. 9
• D. 12

Hint:

For equal roots in a quadratic equation, always set $b^2 - 4ac = 0$ to find the condition.

Answer 1

The Correct Option is D

Step 1: Condition for equal roots.
For equal roots, discriminant $D = 0$. \[ D = b^2 - 4ac = 0 \]
Step 2: Substitute the values.
Here, $a = 3$, $b = -12$, and $c = m$. \[ (-12)^2 - 4(3)(m) = 0 \] \[ 144 - 12m = 0 \Rightarrow m = 12 \]
Step 3: Conclusion.
Therefore, the value of $m$ is 12.