Question

Assertion (A): The quadratic equation $$3kx^{2} - 4kx + 4 = 0$$ has equal roots, if $$k = 3$$.

Reason (R): For equal roots of a quadratic equation, we must have $$\mathrm{D} = 0$$.

Options

• Both A and R are true, and R is the correct explanation of A.

• Both A and R are true, but R is not the correct explanation of A.

• A is true, but R is false.

• A is false, but R is true.

Answer 1

Both A and R are true, and R is the correct explanation of A.

Explanation:

Step 1 – Assertion: A is true. Substituting $$k = 3$$ gives $$9x^{2} - 12x + 4 = 0$$. $$D = (-12)^{2} - 4 \times 9 \times 4 = 144 - 144 = 0$$. Thus, the equation has equal roots.

Step 2 – Reason: R is true. For equal roots, the discriminant must be zero.

Step 3 – Link: The discriminant is zero when $$k = 3$$ and this condition gives equal roots; therefore, R correctly explains A.