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Let alpha,beta be the roots of the equat...

Let `alpha,beta` be the roots of the equation `x^2-p x+r=0` and `alpha/2,2beta` be the roots of the equation `x^2-q x+r=0` , the value of `r` is

A

`2/9(p-q)(2q-p)`

B

`2/9(q-p)(2p-q)`

C

`2/9(q-2p)(2q-p)`

D

`2/9(2p-q)(2q-p)`

Text Solution

Verified by Experts

The correct Answer is:
D
The equation `x^(2)-px+r=0` has roots `(alpha, beta)` and the equation `x^(2)-qx+r` has roots `((alpha)/2, 2beta)`
`impliesr=alpha beta` and `alpha+beta=p` and `(alpha)/2+2beta=q`
`implies(beta=(2q-p)/3` and `alpha-(2(2p-q))/3`
`impliesalpha beta=r=2/9(2q-p)(2p-q)`
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