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Q.

If the roots of x540x4+Px3+Qx2+Rx+S=0  are in G.P. and sum of their reciprocals is 10, then |S|  is:

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a

2

b

61

c

28

d

32

answer is D.

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Detailed Solution

The given roots of the equation x540x4+Px3+Qx3+Rx+S=0 

are in G.P.

Let roots to be a,ar,ar2,ar3,ar4

Sum of the roots : a+ar+ar2+ar3+ar4=40  and

 

Given that, sum of their reciprocals : 1a+1ar+1ar2+1ar3+1ar4 =1+r+r2+r3+r4ar4=40a2r4=10

 a2r4=4  or ar2=±2

Now S= product of roots =a. ar. ar2. ar3. ar4

=a5r10

=(ar2)5

=±32

  |S|=32

 

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