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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 `C/A` is

A

`-k/2`

B

`-k`

C

`k/2`

D

`k`

Text Solution

Verified by Experts

The correct Answer is:
D
`:.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
`:'C/A(alpha beta(gamma+delta)+gamma delta(alpha +beta))/(alpha +beta+gamma+delta)`
`=(k(gamma +delta)+k(alpha+beta))/(alpha+beta+gamma+delta)[ :' alpha beta =gamma delta=k]`
`=k`.v
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