What branch of mathematics is this?

49 Views Asked by At

This is the question: How many real solutions is there to the following equation?

$ x+x^2 +...+ x^{2012} = 0$

The answer is the 2 solutions: $x=0$ and $x=-1$

I solved the question by just factorizing the expression. But I was wondering if these types of problems belong to some category in which you should solve with a specific technique (in case the problem is much harder). If so, what are some good sites to read about it?