Algebraic Numbers

Algebraic numbers are a special category of numbers that are roots of polynomial equations with rational coefficients. This means that if you have a polynomial equation, like \( x^2 - 2 = 0 \), the solutions to this equation, such as \(\sqrt{2}\), are considered algebraic numbers. In simpler terms, they include integers, fractions, and some square roots or cube roots, but not numbers like \(\pi\) or \(e\), which cannot be expressed this way. Algebraic numbers play a crucial role in various fields of mathematics, particularly in number theory and algebra.