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Question

If x2+2ax+a<0, x[1,2] then the values of a lies in the interval

A
(,45)
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B
(,13)
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C
(,13]
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D
(,45]
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Solution

The correct option is A (,45)
Let f(x)=x2+2ax+a
Given:
f(x)<0, x[1,2]
1 and 2 lie between the roots of f(x)=0


Conditions:
(i) f(1)<01+3a<0a<13(1)

(iii)f(2)<04+5a<0a<45(2)

From (1) and (2),
We get a(,45)

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