How Do You Spell POLYNOMIAL EQUATION?

Pronunciation: [pˌɒlɪnˈə͡ʊmɪəl ɪkwˈe͡ɪʒən] (IPA)

The spelling of "polynomial equation" may seem tricky, but it becomes clearer with the use of IPA phonetic transcription. "Polynomial" starts with the voiced plosive /p/, followed by the diphthong /oʊ/ and the nasal sound /l/. Then comes the unvoiced plosive /n/ and the vowel /i/, ending with the unvoiced fricative /əl/. "Equation" starts with the unvoiced plosive /ɪk/, followed by the diphthong /weɪ/, the unvoiced plosive /ʃ/, and finally the nasal sound /ən/. Overall, the spelling of "polynomial equation" aligns with its pronunciation.

POLYNOMIAL EQUATION Meaning and Definition

1. A polynomial equation is a type of mathematical equation that involves the sum of different powers of a variable multiplied by coefficients. It is typically expressed as an algebraic expression comprising terms such as constants, variables, and exponents. The equation follows the general form of a polynomial, which consists of multiple terms added or subtracted together.

   In a polynomial equation, each term consists of a coefficient multiplied by the variable raised to a non-negative integer exponent. The highest exponent in the equation determines the degree of the polynomial. For instance, a quadratic equation is a polynomial equation of degree 2, while a cubic equation is of degree 3.

   The purpose of solving a polynomial equation is to find the values of the variable that satisfy the equation. These values, known as solutions or roots, make the polynomial equation equal to zero. The number of solutions can vary depending on the degree of the polynomial, as real polynomials of odd degree generally have at least one solution.

   Polynomial equations find applications in various fields of mathematics, physics, and engineering. They play a crucial role in algebraic manipulation, curve fitting, optimization problems, and modeling real-world phenomena. Techniques such as factoring, synthetic division, and the quadratic formula are often employed to solve polynomial equations and determine their solutions.

Etymology of POLYNOMIAL EQUATION

The word "polynomial" comes from the Latin words "polynoma" and "polyonyma", which were derived from the Greek words "polus" meaning "many" and "onomaein" meaning "to name". In mathematics, a polynomial is an expression consisting of variables, coefficients, and exponents, with various terms added or subtracted together. The term "equation" comes from the Latin word "aequatio", which means "equalization". Therefore, the term "polynomial equation" refers to an expression involving multiple variables and exponents that is set equal to zero, resulting in an equality.