
Hi Soumya
It is given that f(k) = 1/k for some particular values of x = k.
So for those values of x = k, we have k*f(k) = 1 i.e. k*f(k)  1 = 0
i.e. for some particular values of x, we get x*f(x)  1 as zero. And this x*f(x)  1 is also a polynomial of one higher degree than that of f(x). And the values of x at which this new polynomial becomes zero are its roots.
I hope it helps.
Kamal Lohia
