Question

If f(x)+f(1/1-x)=2(1-2x)/x(1-x) then f(x)=

Answer 1

This is pretty simple. Using basics of remainder theorem, remainder of f(x) when divided with (x-a) will be f(a).

So from the above data, f(-1) = 6 and f(1) = 0.

Substituting it, 3(-1)^4-a(-1)^3+2a(-1)^2-(-1)-b = 6

i.e. 3+a+2a+1-b = 6 => 3a - b = 2

Also 3(1)^4-a(1)^3+2a(1)^2-(1)-b = 0

i.e. 3-a+2a-1-b = 0 => a - b = -2

Solving these two equations, we can get a = 2, b = 4.