34. If the two roots of the equaion...
Question

# 34. If the two roots of the equaion (a - 1)(x + x² +1)+(a + 1)(x² + x + 1) = 0 are rea set of all value of a is +x+1)+(a + 1)(x² + x + 1) = 0 are real and distinct, then the (B) (-2,-2)(2.) JEE Main (Online) 151

JEE/Engineering Exams
Maths
Solution
95
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( (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 ) ar ( x ) is real, ( 1+x+x^{2} eq 0 ) So ( 2 a x-2 x^{2}-2=0 quad Rightarrow quad x=frac{a pm sqrt{a^{2}-4}}{2} ) two roots ane real & distinet, so ( 101>2 ), ( a in(2, infty) cup(-2,-infty) )