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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 correct statement is

A

`C^(2)=AD`

B

`C^(2)=A^(2)D`

C

`C^(2)=AD^(2)`

D

`C^(2)=(AD)^(2)`

Text Solution

Verified by Experts

The correct Answer is:
B
`:.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. (iv) we get
`alpha beta gamma delta =D`
`impliesk.k=D[ :' alpha beta =gamma delta =k]`
`=(C/A)^(@)=D` [from Eq. (v)]
`:.C^(2)=A^(2)D`
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