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Question

Let α and β be the roots of equation px2+qx+r=0,p0. If p,q,r are in A.P. and 1α+1β=4, then the value of |αβ| is

A
619
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B
2179
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C
349
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D
2139
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Solution

The correct option is D 2139
Given,
px2+qx+r=0
α+β=qr, αβ=rp
Now, 1α+1β=4
α+βαβ=qprp=qr=4
q=4r...(1)
As given, p,q,r are in A.P.
2q=p+r...(2)
from equation (1) and (2)
2(4r)=p+r
p=9r
Now, (αβ)2=(α+β)24αβ
=(qp)24rp
=16r2+49rr(9r)2
{q=4r,p=9r}
=2139

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