[Maths Class Notes] on Maths Equations Pdf for Exam

Different Types of Equations:

Below are different types of equations, which we use in algebra to solve them.

1. Linear Equation

2. Quadratic Equation

3. Radical Equation

4. Exponential Equation

5. Rational Equation

Linear Equation:

A linear equation is an equation for a straight line.

Example: y = 2x + 1

  5x – 1 = y

The term involved in the linear equation is either a constant or single variable or a product of a constant. 

Linear equation will be written as:

Y = mx + c, m is not equals to 0.

where,

m is the slope

c is the point on which it cut y-axis

The following are examples of some linear equations:

1. with one variable: 5x – 10 = 2

2. with two variables: 5x + y = 3

Quadratic Equation:

A quadratic equation is a polynomial whose highest power is the square or variable (x2, y2, etc.)

The quadratic equation is a second-order equation in which any one of the variable contains an exponent of 2

The standard form of the quadratic equation is:

 ax2 + bx + c = 0

Where, a, b, c are numbers

a, b are called the coefficients of x² and x respectively, and c is called the constant.

The following are examples of some quadratic equations:

1. x2 + y + 7 = 0 where  a=1, b= 1 and c = 7

2. 2x2– 3y + 3 = 0  where  a= 2, b= -3, c = 3

3. 5x2 + 2y = 0             where a=5, b=2, c= -8

4. 9x2 = 4

        9x2 – 4 = 0  where a= 9, b=0 and c= -4

Radical Equation:

A radical equation is an equation in which a variable is under a radical. 

Methods to solve the radical equations are:

1. Separate the radical expression involving the variable, in case of more than one radical expression, and then separate one of them.

2. Raise both sides to the index of the radical.

Example:

Solve  [sqrt{5a^{2}+3a}] – 2 = 0

Isolate the radical expression.

[sqrt{5a^{2}+3a}]  = 2 

Raise both sides to the index of the radical; in this case, square both sides.

([sqrt{5a^{2}+3a}])2 = ( 2 )2

5a2 + 3a = 4

5a2 + 3a – 4 = 0

Exponential Equation:

Exponential equations have variables in place of exponents. An exponential equation can be solved as:

ax = ay  ; x = y

Example:

2x = 4

The above equation is equivalent to 2x = 22

Rational Equations:

A rational equation involves the rational expressions (in the form of fractions), with a variable, say x, in the numerator, denominator, or both.

Example : [frac{x}{2}] = [frac{x+3}{4}]

Let us solve the equation by cross multiplication and equating the like terms.

So, the rational equation becomes:

4x = 2(x + 3)

4x = 2x + 6

4x – 2x = 6

2x = 6

x = 6/2

x = 3

Examples:

Q. Solve the given equation:

2x – 6(2 – x) = 3x + 2

A:  Simplify the given equation:

2x – 6(2 – x) = 3x + 2

2x – 12 + 6x = 3x + 2

8x = 3x + 14

8x – 3x = 14

5x = 14

x = 14 / 5

Therefore the solution for the given equation 2x – 6(2 – x) = 3x + 2 is 14/5.

Verification:

Substitute x = 14/5 in the given equation 2x – 6(2 – x) = 3x + 2 ;

2(14/5) – 6(2 –  14/5) = 3(14/5) + 2

28 / 5 + 24 / 5 = 52/5

28 + 24 = 52 

52 = 52

L.H.S = R.H.S 

Hence verified.