If the roots of x5−40x4+Px3+Qx2+Rx+S=0  are in G.P. and sum of their reciprocals is 10, then |S|  is:

The given roots of the equation x5−40x4+Px3+Qx3+Rx+S=0 are in G.P.Let roots to be a,  ar, ar2, ar3, ar4Sum 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=±2Now S= product of roots =a. ar. ar2. ar3. ar4=a5r10=(ar2)5=±32∴  |S|=32