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Question

If α,β be the roots of the equation
2x22(m2+1)x+(m4+m2+1)=0
then (α2+β2)=


A

m

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B

0

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C

1

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D

m2

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Solution

The correct option is D

m2


Given:2x22(m2+1)x+(m4+m2+1)=0

α+β=2(m2+1)2=m2+1 ......(i)

and α.β=m4+m2+12 .....(ii)

Using α2+β2 = (α+β)22αβ
From (i) and (ii),
α2+β2=(m2+1)22(m4+m2+1)2
α2+β2=m4+2m2+1m4m21=m2


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