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Question

If α,β are the roots of the equation x2px+r=0 and α2,2β are the roots of the equation x2qx+r=0, then the value of r in terms of p and q is

A
29(pq)(2qp)
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B
29(qp)(2pq)
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C
29(q2p)(2qp)
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D
29(2pq)(2qp)
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Solution

The correct option is D 29(2pq)(2qp)
Since α,β are the roots of x2px+r=0
α+β=p and αβ=r
It is given that α2 and 2β are the roots of the equation x2qx+r=0
α2+2β=q and
α2×2β=r
Solving
α+β=pα2+2β=q
3α2=2pqα=23(2pq)β=13(2qp)

We know that,
r=αβr=29(2pq)(2qp)

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