Hi. :)
It is none of the above because of the following reason:
Suppose a = 0, b = 1, c = 99, d = 100
Option(i): if both the roots are in [a,b] = [0,1] then the expression (x-c) + (x-d) will be very large which won't make this expression (x-a) + (x-b) + (x-c) + (x-d) equal to zero.
Same analysis for other options
:)