Question

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

• A. $4$
• B. $7$
• C. $9$
• D. $12$

Hint:

For a quadratic equation to have equal roots, its discriminant must be zero. Use the formula $\Delta = b^2 - 4ac$.

Answer 1

The Correct Option is D

Step 1: Use the condition for equal roots.
For a quadratic equation $ax^2 + bx + c = 0$ to have equal roots, the discriminant must be zero. The discriminant is given by: \[ \Delta = b^2 - 4ac \]
Step 2: Apply the formula to the given equation.
For the equation $3x^2 - 12x + m = 0$, we have: \[ a = 3, \quad b = -12, \quad c = m \] So, the discriminant is: \[ \Delta = (-12)^2 - 4(3)(m) = 144 - 12m \]
Step 3: Set the discriminant equal to zero for equal roots.
\[ 144 - 12m = 0 \] \[ 12m = 144 \] \[ m = 12 \]
Step 4: Conclusion.
Hence, the value of $m$ is $12$.