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alpha,beta be the roots of the equation ...

`alpha,beta` be the roots of the equation `x^2-px+r=0` and `alpha/2 , 2beta` be the roots of the equation `x^2-qx+r=0` then value of `r` is

A

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

B

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

C

`2/9(p-2q)(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=0` has roots `(alpha)/(2),2 beta.`
`impliesr =alphabetaand alpha+beta=p,`
`and (alpha)/(2)+2beta=qimpliesbeta=(2q-p)/(3)and alpha=(2(2p-q)/(3)`
`impliesalphabeta=r=2/9(2q-p)(2p-q)`
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