I was bothered with the following very simple problem:
Solving a quadratic equation $x^2+x+1=0$ in mathematica
if I use "solve" function in mathematica as below:
Solve[x^2 + x + 1 == 0, x]
I will get very weird solutions
$$x = -(-1)^{1/3}; \;\;\; x = (-1)^{2/3}.$$
However, instead of using $\;$Solve[x^2 + x + 1 == 0, x], I use
Solve[a * x^2 + b * x + c == 0, x]
and then substituting back $a=b=c=1$, then I can get the correct roots (which I expect to see...); i.e., I obtain $$ x_{1,2} = \frac{-1 \pm i\sqrt{3}}{2}. $$
It seems to me I get different solutions which really bothers me alot. Did I miss anything? or can anyone help to explain why this situation could happen? By the way, my mathematica version is 10.3.0.0