> As for formulas: no, there is no GENERAL formula for the quintic polynomial or higher. Note that there is no general formula for quintics (and higher) in rad

> As for formulas: no, there is no GENERAL formula for the quintic polynomial or higher. Note that there is no general formula for quintics (and higher) in radicals. But it is a bit arbitrary to draw the line there. There is also no 'general formula' using basic arithmetic operations (addition, subtraction, multiplication, division) that gives roots for x^2 = 2. However it is quite useful to be able to talk about those roots, so we added a dedicated symbol for them (sqrt), and more generally extended the definition of exponentiation to fractional powers. If it were generally useful to talk about the roots of quintics we also would've added common notation for their roots.