Question

The value of m for which the quadratic equation $3x^2 - 7x + m = 0$ has real and equal roots, is

• A. $7$
• B. $\frac{49}{12}$
• C. $\frac{49}{3}$
• D. $4$

Hint:

For any quadratic equation $ax^2 + bx + c = 0$ to have real and equal roots, remember the direct condition $b^2 = 4ac$.
This allows you to quickly set up the equation and solve for the unknown parameter without extra intermediate steps.

Answer 1

The Correct Option is B

Step 1: Recall the condition for equal roots.
A quadratic $ax^2+bx+c=0$ has real, equal roots exactly when $b^2 = 4ac$.
Step 2: Identify the coefficients.
Here $a=3$, $b=-7$, $c=m$, so we need
\[ (-7)^2 = 4(3)(m) \]
Step 3: Solve for $m$.
\[ 49 = 12m \implies m = \frac{49}{12} \]
Step 4: Conclude.
This matches option (2).
\[ \boxed{\frac{49}{12}} \]