The number of imaginary roots of $\sum_{n=1}^{100} \frac {n^2}{x-x_{n} }= 101$, where each $x_n$ is real 
Determine the number of imaginary roots of the equation
$$\sum_{n=1}^{100} \frac {n^2}{x-x_{n} }= 101$$
where $x_{1}$, $x_{2}$, $x_{3}$, $\ldots$ are all real.

I did this question a few months back, but I am not able to do this question now.
Also, if anyone has seen this question before, please let me know its source.

I think the question is ambiguous about whether it asks for purely imaginary roots or merely for complex roots that are not real.
But let's take a look to see what kind of roots we can find.
Let $x$ be a complex number. Suppose the imaginary part of $x$ is positive.
For $n$ an integer and $x_n$ real,
what can you say about the imaginary part of
$$
\frac {n^2}{x-x_{n}}?
$$
Now add up a hundred terms in that form. What conditions will make the sum equal to $101$?
