How to solve Nth-degree polynomial equation with terms only in N, 1 and 0?

Question

Namely, an equation like this:

ax^n + bx + c = 0

Answer 1

This is often called a depressed $n$th-power (i.e. cubic, quartic, &c.) equation

• $n=2$ is trivial.
• $n=3$, you can use the cubic formula, or Cardano's method is designed for this case.
• $n=4$ also has a formula, and a corresponding method.
• $n=5$ can be expressed in terms of elliptic functions (which I only learnt yesterday, as it happens).
• $n \geq 6$, see this question.