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Question

Let α (a) and β (b) be the roots of the equation of
(31+a)1)x2+(1+a)1)x+(61+a)1)=0,a>1
Then lima0 α(a) and lima0 β(a) are

A
52 and 1
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B
12 and 1
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C
72 and 2
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D
92 and 3
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Solution

The correct option is B 12 and 1
[(1 + a)13 -1)x2 + [(a+1)12 -1] x + [(a+1)16-1] =0
Let 1 + a = p6.
Then (p2 -1) x2 + (p3 -1) x + (p -1) = 0
(p + 1)x2 +(p2 +p + 1)x+1 = 0
As a 0, p 1
2x2+3x + 1 = 0 x = -1 and x = 12

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