Lecture #1 : Basic Mathematics : Linear & Quadratic Equations

 (1) Linear Equations 

A linear equation is an equation of the form 

                              ax + b = 0

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Solving Linear Equations

Example 1:

3x + 4 = 0

 3x = - 4

x = - 4/3

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Example 2:

4x + 5 = 6(x + 1) + 7

4x + 5 = 6x + 6 + 7

4x + 5 = 6x + 13

4x - 6x = - 5 + 13

- 2x = 8

x = - 4

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Example 3 :

2x + 6 = 3(x - 2) + x

2x + 6 = 3x - 6 + x

2x + 6 = 4x - 6

2x - 4x = - 6 - 6

- 2x = - 12

x = 6

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Example 4:

(x-2)/5 - (x-4)/2 = 2

2(x-2) -5(x-4) = 20 

2x - 4 - 5x + 20 = 20 

-3x + 16 = 20

-3x = 20-16

x = -4/3 

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(2) Quadratic Equations :-

A quadratic equation is an equation of degree two, written as:

                      ax^2 + bx + c = 0

There are three methods to solve quadratic equations:

1. Factorization Method

2. Completing the Square

3. Quadratic Formula

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Factorization Method

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Example 1:

x² - x - 6 = 0

x² - 3x + 2x - 6 = 0

x ( x - 3) + 2 (x - 3) = 0

( x + 2 ) ( x - 3 ) = 0

x + 2 = 0.         Or        x - 3 = 0

x = -2                            x = 3

Solution Set Of X = { -2 ,3}

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Example 2:

x²- 7x+12 = 0

x²-4x-3x + 12 = 0

x(x-4)-3(x-4)=0

(X-3)(x-4) = 0

x-3=0          or       x-4=0

x=3.                        x=4

Solution Set Of X = {3,4}

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Summary:-

A linear equation has a variable of power 1.

A quadratic equation has a variable of power 2.

The main methods to solve quadratic equations are Factorization, Completing the Square, and Quadratic Formula.

The solution set represents all values of that satisfy the given equation.

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Prepared by: Saif Ullah

Course: Basic Mathematics

Instructor: Prof. Mubeen Ali

Program: BB

A (1st Semester)

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