If $\alpha$ is a repeated root of $ax^{2} + bx + c = 0$, then $\lim_{x \rightarrow \alpha}\frac{\sin{(ax^{2} + bx + c)}}{(x - \alpha)^{2}}$ is

Question

Dr. Abubacker · Accepted Answer

(b)
Since, $\alpha$ is a repeated root.
$	herefore\ \ \ \ \ ax^{2} + bx + c = a(x - \alpha)^{2}$
Now, $\lim_{x ightarrow \alpha}\frac{\sin{(ax^{2} + bx + c)}}{(x - \alpha)^{2}}$
$= \lim_{x ightarrow \alpha}\frac{\sin{a(x - \alpha)^{2}}}{a(x - \alpha)^{2}} 	imes a$
$= \lim_{x ightarrow \alpha}{a(1) =}a$

Q. If $\alpha$ is a repeated root of $ax^{2} + bx + c = 0$, then $\lim_{x \rightarrow \alpha}\frac{\sin{(ax^{2} + bx + c)}}{(x - \alpha)^{2}}$ is

Explanation

Reviewed by Dr. Abubacker

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