The number of values of a for which (x^2+x+1)a^2-(x^2+2)a-3(2x^2+3x+1)=0 will be an identity in x is

JEE Advanced Mathematics question

The number of values of for which

+x+-+2)a-+3x+1)=0

will be an identity in is

Answer: (A)

Collect powers of :

-a-+-9)x+-2a-3)=0.

For an identity in all three coefficients must vanish: -

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Question ID VK-110191