binary quadratic (english) - meaning, definition, translation, pronunciation

Part of Speech

• Adjective: binary
• Adjective: quadratic

Phonetic Transcription

/bɪˈnɛəri/ /kwɒdˈrætɪk/

Meaning and Usage

The term "binary quadratic" refers to a specific type of mathematical expression or equation that involves two variables and terms raised to the second power (squared). It is often used in the context of algebra and number theory.

• Binary: relating to or consisting of two parts, often used in mathematical contexts to denote systems or equations having two variables or components.
• Quadratic: relating to or denoting an equation of the second degree, typically in the form ax² + bx + c = 0, where a, b, and c are constants.

Frequency of Use

The term "binary quadratic" is relatively specialized and is mainly found in written mathematical contexts rather than in everyday oral speech. It is used frequently in academic papers, textbooks, and discussions related to mathematics and computer science, particularly in number theory and optimization problems.

Example Sentences

1. The researcher proposed a new algorithm based on binary quadratic programming to optimize resource allocation.
   Исследователь предложил новый алгоритм, основанный на бинарном квадратичном программировании для оптимизации распределения ресурсов.

2. Solving binary quadratic equations can be quite challenging without the right tools.
   Решение бинарных квадратичных уравнений может быть довольно сложным без правильных инструментов.

3. The properties of binary quadratic forms are essential in understanding various number theory concepts.
   Свойства бинарных квадратичных форм являются важными для понимания различных понятий теории чисел.

Idiomatic Expressions

The phrase "binary quadratic" does not have widely recognized idiomatic expressions due to its specialized nature in mathematical discourse. However, other terms related to "binary" and "quadratic" can have idiomatic uses in different contexts.

Example Idiomatic Use (Binary)

1. In the binary world of technology, decisions are often made swiftly.
   В бинарном мире технологий решения часто принимаются быстро.

2. The game is defined in binary terms: win or lose, yes or no.
   Игра определена в бинарных терминах: выигрыш или проигрыш, да или нет.

Example Idiomatic Use (Quadratic)

1. The relationship between these two variables is not linear; it's quadratic.
   Связь между этими двумя переменными не линейная; она квадратичная.

2. Finding solutions requires a quadratic approach rather than a simple linear method.
   Нахождение решений требует квадратичного подхода, а не простого линейного метода.

Etymology

The word "binary" comes from the Latin word bini, which means "two by two," or "pair." The term "quadratic" derives from the Latin quadratus, meaning "square," which relates to the second-degree polynomial expressions.

Synonyms and Antonyms

• Synonyms:
• For binary: dual, twofold, double

• For quadratic: second-degree, square, polynomial of degree two

• Antonyms:

• For binary: singular, individual
• For quadratic: linear (referring to first-degree functions or equations)