If the roots `x^5-40 x^4+P x^3+Q x^2+R x+S=0` are n G.P. and the sum of their reciprocals is 10, then `|S|` is `4` b. `6` c. `8` d. none of these

Options

A. 4
B. -4
C. 8
D. none of these

Answer

D

Explanation

Let the roots be `(a)/(r^(2)), (a)/(r), a, ar, ar^(2)` Then,
`a((1)/(r^(2))+(1)/(r)+1+r+r^(2))=40" "...(i)`
It is given that
`(1)/(a)(r^(2)+r+1+(1)/(r)+(1)/(r^(2)))=10" "...(i)`
From (i) and (ii), we get
`a^(2) = 4 rArr a = +- 2`
Now,
Product of the roots = -S
`rArr" "a^(5) = - S rArr S = +- 32 rArr |S| = 32`