Question 2

Step 1 · Apply Discriminant Condition and Solve for $k$

Comparing $2x^2 + kx + 3 = 0$ with $ax^2 + bx + c = 0$: $a = 2, \quad b = k, \quad c = 3$

For two equal roots, the discriminant must be zero ($b^2 - 4ac = 0$):

Step 1 · Expand and Apply Discriminant Condition

Expanding the equation: $kx^2 - 2kx + 6 = 0$

Comparing with $ax^2 + bx + c = 0$: $a = k, \quad b = -2k, \quad c = 6$

For two equal roots, $b^2 - 4ac = 0$:

Step 2 · Solve for $k$ and Check Validity

From $4k(k - 6) = 0$: $4k = 0 \quad \text{or} \quad k - 6 = 0 \implies k = 0 \quad \text{or} \quad k = 6$

If $k = 0$, the original equation simplifies to $6 = 0$, which is not a quadratic equation ($a \ne 0$).

Therefore, $k \ne 0$, leaving: $k = 6$