Hello guys I have a simple question to ask. For example I have the equation :
$$x^n + x^{n-1} + x^{n-2} + ... + 1 = 0$$
I read somewhere that the number of solutions to an equation is given by the biggest power in the equation. So in the equation above, there should be $n$ solutions. Is this correct ? If it is, can anyone provide a proof?
The solutions are counting multiplicity and include complex solutions.
It's called the fundamental theorem of algebra. Low-level proofs are not easy to come by, however.