If $\alpha$ is a repeated root of $ax^2 + bx + c = 0$, then $\lim_{x \to \alpha} \frac{\sin(ax^2 + bx + c)}{(x - \alpha)^2}$ is
- A. $0$
- B. $a$
- C. $b$
- D. $c$
✅ Correct Answer: $a$
Explanation
Since for repeated root $ax^2 + bx + c = a(x - \alpha)^2$, limit becomes $\sin(a(x - \alpha)^2)/(x - \alpha)^2 \to a$.
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