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Gajendra Banik
Asked: 2022-11-10T22:47:28+05:30 In:

`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)(2q-p)`
B. `(2)/(9)(q-p)(2p-q)`
C. `(2)/(9)(q-2p)(2q-p)`
D. `(2)/(9)(2p-q)(2q-p)`

`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)(2q-p)`
B. `(2)/(9)(q-p)(2p-q)`
C. `(2)/(9)(q-2p)(2q-p)`
D. `(2)/(9)(2p-q)(2q-p)`
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1 Answer

  1. Correct Answer – D
    Since `alpha, beta` are the roots of `x^(2) – px + r = 0`
    `therefore” “(alpha)/(2)+2beta = q and (alpha)/(2) xx 2 beta r`
    Solving `alpha + beta = p and (alpha)/(2)+2 beta = q`, we get
    `alpha =(2)/(3)(2p-q) and beta = (1)/(3)(2q-p)`
    `therefore” “alpha beta = r rArr r = (2)/(9) (2p-q) (2q-p)`

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