Question

If the roots of the equation \(3x^2 + 5x - q = 0\) are equal, then the value of \(q\) will be

• A. $-\dfrac{25}{12}$
• B. $-\dfrac{25}{9}$
• C. $\dfrac{9}{25}$
• D. $-\dfrac{12}{25}$

Hint:

For equal roots, always apply the discriminant condition \(D = 0\).

Answer 1

The Correct Option is B

Step 1: Recall the condition for equal roots.
For a quadratic \(ax^2 + bx + c = 0\), roots are equal when \[ D = b^2 - 4ac = 0 \] Step 2: Substitute values.
Here, \(a = 3, b = 5, c = -q\). \[ b^2 - 4ac = 0 \implies 25 - 4(3)(-q) = 0 \] Step 3: Simplify.
\[ 25 + 12q = 0 \Rightarrow q = -\dfrac{25}{12} \] Step 4: Verify given options.
Correct answer matches option (A) $-\dfrac{25}{12}$. (Note: If the printed options differ, the logic confirms this value.)