rootswhether

Rootswhether is a term used in mathematical and linguistic discussions to denote a question about the roots of a given function or equation. It is a portmanteau of roots and whether, and it does not have a single, universally accepted definition. In practice, rootswhether serves as a placeholder for evaluating root-related conditions.

Origin and usage: The term has appeared primarily in online glossaries, speculative notes, and some teaching contexts since the 2010s. It is considered informal or provisional and is not standard mathematical vocabulary. In mathematics, writers may employ rootswhether to describe a boolean test that checks whether the roots satisfy a specified property, such as lying in a particular interval or being real.

Definition and variants: A common informal formulation is rootswhether(p, S) = true if all real roots of the polynomial p lie within a set S; variants may ask whether there exists at least one root in S, or whether all roots are real versus complex. The concept is deliberately general and can be adapted to other functions beyond polynomials. For example, if p(x) = x^2 − 5 and S = [−3, 3], the roots are ±√5, approximately ±2.236, which both lie in S, so rootswhether(p, S) would be true.

Relation to formal mathematics: Because rootswhether lacks a formal, widely accepted definition, it is often discouraged in rigorous contexts in favor of precise statements such as p has a root in [a,b] or all roots lie in [a,b]. It remains a useful shorthand in informal discussions and pedagogical materials.

See also: polynomial, root, interval, boolean value.