Polynomial Equations: Concepts, Definition, Formula and Types
Polynomial Equations: This article is an informative source for students to understand the definition, formula, calculation and more for the Polynomial Equations
Polynomial equations are fundamental concepts in mathematics that define relationships between numbers and variables in a structured manner. In mathematics, various equations are composed using algebraic expressions. Polynomials represent a specific type of algebraic equation.
What is a Polynomial Equation?
The equations formed with variables, exponents and coefficients are called polynomial equations. It can have different exponents, where the higher one is called the degree of the equation. We can solve polynomials by factoring them in terms of degree and variables present in the equation.
A polynomial function is an expression which consists of a single independent variable, where the variable can occur in the equation more than one time with a different degree of the exponent. Students will also learn here how to solve these polynomial functions. The graph of a polynomial function can also be drawn using turning points, intercepts, end behavior and the Intermediate Value Theorem.
Polynomial Equations Formula
Example of a polynomial equation is: 2x2 + 3x + 1 = 0, where 2x2 + 3x + 1 is basically a polynomial expression which has been set equal to zero, to form a polynomial equation.
Types of Polynomial Equation
A polynomial equation is basically of four types;
- Monomial Equations
- Binomial Equations
- Trinomial or Cubic Equations
- Linear Polynomial Equations
- Quadratic Polynomial Equations
- Cubic Polynomial Equation
Monomial Equation:
A monomial equation, also known as a linear equation, consists of only one variable term. It can be expressed algebraically as:
ax + b = 0
Binomial Equations:
An equation that consists of two variable terms and a constant term is known as a binomial equation, often seen in the form of a quadratic equation. It can be expressed algebraically as:
ax2 + bx + c = 0
Trinomial Equations:
An equation that includes three terms with variables, followed by a quadratic and linear term, is known as a trinomial equation. This type of equation is also referred to as a cubic equation because it involves a polynomial of degree three. In mathematical terms, a cubic polynomial equation is expressed as:
ax3 + bx2 + cx + d = 0
Quadratic Polynomial Equation
A polynomial equation with a degree of two is known as a quadratic equation. It can be expressed algebraically as:
ax2 + bx + c = 0 ; a ≠ 0
Check:
Relations and Functions
Determinants and Matrices
Profit And Loss
Anisha Mishra is journalist with over 3 years of experience in covering the Indian education sector. She has worked extensively in the K12 domain, with focus on the state board as well as central board examinations, policy structure of seconday and higher secondary education as well as the entrance examinations like JEE, NEET, CLAT, etc. Her extensive experience in the domain has helped her provide students with concise accurate information in all aspectes of school life and education. Her key interest lies in decoding the changes in the curriculum, NEP implementation and changing education ecosystem in the country. Besides working, she enjoys traveling, exploring new places and cultures, and painting.
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