If $ \lim _{x \rightarrow 1} \frac{a x^{2}+b x+c}{(x-1)^{2}}=2 $, then $ (a, b, c) $

Question

If $ \lim _{x \rightarrow 1} \frac{a x^{2}+b x+c}{(x-1)^{2}}=2 $, then $ (a, b, c) $, $ (2,-4,2) $, $ (2,4,2) $, $ (2,4,-2) $, $ (2,-4,-2) $

MARKS App · Accepted Answer

Given, lim x → 1 ⁡ a x 2 + b x + c x - 1 2 = 2 This limit will exist, if a x 2 + b x + c = 2 x - 1 2 ⇒ a x 2 + b x + c = 2 x 2 - 4 x + 2 ⇒ a = 2 , b = - 4 , c = 2

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