Types of Equations and Examples

Types of Equations and Examples

There are various types of equations, such as,

1. Linear equation

  • Equation with  one variable
  • Equation with two variables
  • Equation with three variables

2. Quadratic equation

3. Polynomial equation

  • Monomial Equations
  • Binomial Equations
  • Trinomial Equations

4. Trigonometric equation

5. Radical equation

6. Exponential equation

7. Rational equation

1. Linear Equation: 

A linear equation is an algebraic equation. In linear equation, each term is either a constant or the product of a constant and a single variable. If there are two variables, the graph of linear equation is a straight line.

General form of the linear equation with two variables is given below:-

y = mx + c, m  0.

  • Equation with one Variable: An equation who have only one variable, e.g.
  1. 12x – 10 = 0
  2. 12x = 10
  • Equation with two Variables: An equation who have two variables, e.g.
  1. 12x +10y – 10 = 0
  2. 12x +23y = 20
  • Equation with three Variables: An equation who have three variables, e.g.
  1. 12x +10y -3z – 10 = 0
  2. 12x +23y – 12z = 20

2. Quadratic Equation:

It is the second degree equation in which one variable contains the variable with an exponent of 2. Its general form is

ax2 + bx + c = 0, a  0

Examples of Quadratic Equations:

  1. 12x2 + 10x – 40 = 0
  2. 23y2 – 4y + 12 =0

3.Polynomial Equation:

Polynomial Equation can be expressed in terms of monomial, binomial, trinomial and higher order polynomials. It may contain on both positive and negative values. Polynomials may also contains on decimal values.

Types of Polynomial Equations

There are following three types of polynomial equations:
  • Monomial Equations
  • Binomial Equations
  • Trinomial Equations

Monomial Equations: The polynomial equations which has only one term is called as monomial equations. e.g.

12x = 0

-2xy = 0

Binomial Equations: The polynomial equations which has two terms is called as binomial equations. e.g.

12x2 + 4y= 0

27x– 19 = 0

Trinomial Equations: The polynomial equations which has three terms is called as trinomial equations. e.g.

10xy + 23y – 2x = 0

3x– 3 + 2x = 0

4. Trigonometric equation: 

These equations contains a trigonometric function. So, first we must have to introduce the trigonometric functions to explore them thoroughly. Only few simple trigonometric equations can be solved without any use of calculator but not at all. In some cases, inverse trigonometric functions are valuable.

5. Radical Equation:

It is an equation whose maximum exponent on the variable is 1/2 and have more than one term or a radical equation is an equation in which the variable is lying inside a radical symbol usually in a square root.

Examples of Radical equations:

x1/2 + 14 = 0

(x+2)1/2 + y – 10

6. Exponential equation:

It is an equation who have variables in the place of exponents. This can be solved using the property: ax=ay=> x = y.

Examples of exponential euqations 

  1. xa = 0 Here “x” is base and “a” is exponent.
  2. 10x =0
  3. 8a = 64

7. Rational Equations: 

A rational equation is one that involves rational expressions.

Example of Rational Equations:

x/4 = (x+12)/12