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If alpha is a repeated root of ax^2+bx +...

If `alpha` is a repeated root of `ax^2+bx +c=0` , then `lim_(xrarralpha)(sin(ax^2+bc+c))/(x-alpha)^2` is equal to

A

0

B

a

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b

D

c

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The correct Answer is:
B
Since `alpha` is a repeated root of `ax^2+bx +c=0`.
` therefore ax^2+bx +c=a(x-alpha)^2`
Now,
` lim_(xtoalpha)sin(ax^2+bx+c)/(x-alpha)^2`
`lim_(xtoalpha)(sina(x-alpha)^2)/(x-alpha)^2=alim_(xtoalpha)(sina(x-alpha)^2)/(a(x-alpha)^2=axx1=a)`.
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