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 (2007

Question

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 (2007

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 (2007, 3M) `2/9(p-q)(2q-p)` (b) `2/9(q-p(2p-q)` `2/9(q-2p)(2q-p)` (d) `2/9(2p-q)(2q-p)`
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)`

Monjur Alahi

4 views

2025-01-04 04:42

1 Answers

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Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

Salim Ahmed Kawsar

Correct Answer - 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)`

4 views Answered 2023-02-05 15:29