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Question

Let α and β be the roots of x26x2=0 with α>β if an=αnβn for n1 then the value of a102a83a9=

A

1

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B

2

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C

3

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D

4

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Solution

The correct option is D. 2

Given:

α and β be the roots of x26x2=0

α26α2=0

α2=6α+2

α2=6(α)21+2(α)22

α10=6(α)101+2(α)102

α10=6α9+2α8-------(1)

β26β2=0

β10=6β9+2β8-------(2)

substract eq (2) from eq (1)

α10β10=6(α9β9)+2(α8β8)

a10=6a9+2a8 [an=αnβn]

a102a8=6a9

a102a8=2×3a9

a102a83a9=2


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