Topic 2

EQUATIONS, INEQUALITIES AND ABSOLUTE VALUE

QUADRATIC EXPRESSION AND EQUATION
INEQUALITIES
ABSOLUTE VALUES

QUADRATIC EXPRESSION AND EQUATION
Objectives:
Define quadratic expressions and equation
Solve quadratic equations by factorization, completing the square methods and formula

QUADRATIC EXPRESSION AND EQUATION Eg :

Solving Quadratic Equations Quadratic equations can be solved by the following methods a) when can be factorized b) when cannot be factorized

a) when can be factorized Example 1: Solve the equation Solution: Factorizing The solution set is { -2 , 3/2 }

b) when cannot be factorized
completing the square
formula

completing the square
Solve the equation
Solution: The solution set is {1.162, -5.162}

Test your power!!!!
Solve the equation
Answer:{1.781, -0.281}

Method using formula

Example 3 Solution: The solution set is ????

Test your power again !!!!

TYPES OF ROOTS OF A QUADRATIC EQUATION
Objectives:
Recognize the type of roots based on the discriminant
Relate the roots
Form a quadratic equations using identities

From the general equation, the types of the roots can be determined based on the value of the discriminant,
If
If
If

Example Determine the nature of the roots 1. 2. 3.

Example

THE RELATIONSHIP BETWEEN THE ROOTS, and THE COEFFICIENTS OF A QUADRATIC EQUATION.

In general

Important Identities:

Example

Solution The equation has roots Therefore,

To find a quadratic equation given the roots, the sum and product of the roots need to be found. For example, the quadratic equation with roots 3 and 5 is

Example Given that are the roots of the quadratic equation , find quadratic equation with roots

Again…test your power!!!!!!!!!!!

HOSTEL/WEEKEND JOBS

INEQUALITIES Objectives:
Relate the properties of inequalities
Define and solve linear inequalities
Define quadratic inequalities and solve them using graphical method
Solve the quadratic by using analytical method:
(i) Basic definition
(ii) Real number line
(iii) Table of signs.
Understand and solve rational inequalities involving linear and
quadratic expressions.

LINEAR INEQUALITIES

Topic 2

by Fizaril Amzari Omar

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