Question

( (a-1)left(x^{2}+x+1right)^{2}-(a+1)left(x^{4}+x^{2}+1right)=0 )
( (a-1)left[left(x^{4}+x^{2}+1right)+2 xleft(x^{2}+x+1right)right]-(a+1)left(x^{4}+x^{2}+1right)=0 )
( 2 a xleft(1+x+x^{2}right)-2left(x^{4}+x^{3}+x^{2}+x^{2}+x+1right)=0 )
( 2 a xleft(1+x+x^{2}right)-2 x^{2}left(x^{2}+x+1right)-2left(x^{2}+x+1right)=0 )
as ( x ) is real, ( 1+x+x^{2} eq 0 ) So ( 2 a x-2 x^{2}-2=0 Rightarrow x=a pm sqrt{a^{2}-4} )
two roots ane real se distinct, so ( |a|>2 ), ( a in(2, infty) cup(-2,-infty) )

# 34. If the two roots of the egi 1 x + x 2 -x + 1) = 0 are real and distinct, then the set of all value of a is (B) (-0, - 2) (2.) (D)(0) LJEE Main (Online: 131 JEE Main Batines 15)

Solution