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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


Your Answer
A
619
Your Answer
B
2179
Your Answer
C
349
Correct Answer
D
2139

Solution

The correct option is C 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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