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If alpha, beta, gamma, delta are the roo...

If `alpha, beta, gamma, delta` are the roots of the equation `x^(4)+Ax^(3)+Bx^(2)+Cx+D=0` such that `alpha beta= gamma delta=k` and A,B,C,D are the roots of `x^(4)-2x^(3)+4x^(2)+6x-21=0` such that `A+B=0` The value of `(alpha+beta)(gamma+delta)` is terms of B and `k` is

A

`B-2k`

B

`B-k`

C

`B+k`

D

`B+2k`

Text Solution

Verified by Experts

The correct Answer is:
A
`:.alpha + beta+gamma +delta=-A`……………..i
`(alpha+beta)(gamma+delta)+alpha beta+gamma delta =B`…………..ii
`alpha beta(gamma+delta)+gamma delta(alpha +beta)=-c`……iii
and `alpha beta gamma delta =D`……iv
From Eq. (ii) we get
`(alpha+beta)(gamma+delta)=B-(alpha beta+gamma delta)=B-2k[ :' alpha beta=gamma delta =k]`
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