Question

If the roots of `x^(5) - 40 x^(4) + Px^(3) + Qx^(2) + Rx + S = 0` are in G.P. and sum of their reciprocals is 10, then |S| is equal to
A. 4
B. -4
C. 8
D. none of these

Answer 1

Correct Answer - D
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`