Fun fact: “proper” polynomials have only non-negative integer exponents but you can construct other non-linear polynomial-like equations with negative and even

Fun fact: “proper” polynomials have only non-negative integer exponents but you can construct other non-linear polynomial-like equations with negative and even rational exponents. They work the same with the number of real roots related to the number of coefficient sign changes. Just don’t expect any general solutions, you have to solve them numerically if they don’t simplify to a common type.