Theory of Equations: Introduction

Variables: In mathematics, a variable is represented by a symbol that can be changed according to the problem. The common symbols used to represent variables are \(x\), \(y\), and \(z\).

Constants: In mathematics, a constant is a fixed and known value that can not be changed, commonly constants are represented by numbers and symbols \(a\), \(b\), and \(c\).

Example: \(2x + y = 25\)

Here \(x\), and \(y\) are variables whereas 2 and 25 are constants.

Algebraic Expression: The expression made by using variables and constants with the help of operators (+, -, \(\times\), \(\div\)) is called an algebraic expression.

Example: \(ax^2 + bx + c\)

Here a, b, and c are constants, and \(x\) is a variable.

Algebraic Function: An algebraic expression is called an algebraic function of a variable (\(x, y, z\)) and it is commonly represented by \(f(x)\), \(f(y)\), \(f(z)\) etc.

Example: \(f(x) = 2x^2 + 3x + 1\)

Polynomial Expression: It is an algebraic expression with finite terms and for each term, the exponent of the variable should be positive.

Example: \(3x^2 + 2x + 1\)

Here 1, 2, and 3 are constants whereas \(x^2\) and \(x\) are variables with positive exponents.

Rational Function: A rational function is the ratio of two polynomials where denominator cannot be zero.

Example: \(f(x) = \frac{x^2 + 2}{x^2 + 1}\)

Here \(x^2 + 1\) can not be equal to zero.

Theory of Equations

Chapter 1: Introduction

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