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Question

If the roots of the equation (a1)(x2+x+1)2=(a+1)(x4+x2+1) are real and distinct, then a belongs to

A
(,3]
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B
(,2)(2,)
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C
[2,2]
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D
ϕ
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Solution

The correct option is D ϕ
x4+x2+1=(x2+1)2x2
=(x2+x+1)(x2x+1)

x2+x+10, xR
(a1)(x2+x+1)2=(a+1)(x4+x2+1)
(a1)(x2+x+1)=(a+1)(x2x+1)
x2ax+1=0
The roots are real and distinct.
So, D=a24>0
a(,2)(2,)

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