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Question

If α,β are the roots of x2x+3=0, then α4+β4=

A
10
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B
7
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C
10
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D
8
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Solution

The correct option is D 7
x2x+3=0
Here, a=1,b=1,c=3
αβ=ca=31=3 ----- ( 1 )
α+β=ba=(1)1=1 ---- ( 2 )
(α+β)2=α2+β2+2αβ
(1)2=α2+β2+2(3) [ From ( 1 ) and ( 2 ) ]
1=α2+β2+6
α2+β2=5 ---- ( 3 )
α4+β4=(α2+β2)2α2β2
=(5)22(3)2=7

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