Chapter I

This chapter deals with equations which are classified according to the highest

power of its variable. An equation in the variable x whose highest power is 2 is called a

quadratic equation. It will be observed here that variable a, b and c are real numbers

and a cannot be 0.

TARGET SKILLS:

At the end of this chapter, students are expected to:

• identify quadratic equation;

• discuss real numbers and standard form of the quadratic equation;

• express quadratic equation in standard form; and

• apply distributive property in solving quadratic equation.

Lesson 1

Identifying the quadratic

equation

OBJECTIVES:

At the end of this lesson, students are expected to:

define the quadratic equation;

discuss real numbers in quadratic equation; and

improve writing the standard form of the quadratic equation.

Polynomials are classified according to the highest power of its variable. A first

degree polynomial, like 2x + 5 is linear; a second degree polynomial, like x2 + 2 – 3 is

quadratic; a third degree polynomial, like x3 + 4x2 – 3x + 12 is cubic.

Similarly, equation and inequalities are classified according to the highest power

of its variable. An equation in the variable x whose highest power is two is called a

quadratic equation. Some examples are x2 – 64, 4n2 = 25, 3x2 – 4x + 1 = 0.

Any quadratic equation can be written in the form ax2 + bx + c = 0. This is also

called the standard form of the quadratic equation. Here, a, b and c are real numbers

and a cannot be 0.

Example A. Express x2 = 8x in standard form

x2 = 8x can be written as x2 - 8x = 0

An equation of the form ax2 + bx + c = 0, where a, b and c are constant and a not equal to 0, a id a quadratic equation.

where a=1, b= ˉ8, and c=0.

Example B. Express x2 = 64 in standard form

x2 = 64 can be written as x2 – 64 = 0

where a=1. B=0, and c=ˉ64.

Example C. Express the fractional equation x = 1/x-3 as a quadratic equation.

x = 1/x-3

x (x-3) = 1 multiply both sides by x-3

x² - 3x = 1 using the distributive property

x² - 3x - 1 = 0 a=1, b=ˉ3, c=ˉ1

Exercises:

Which of the following equations are quadratic?

1. 3x = x² - 5

2. 2x =1

3. x² = 25

4. 2x - 3 = x + 5

5. 5x – 2y = 0

Name: ___________________ Section: _______

Instructor: ________________ Date: _______ Rating: ____

Instruction: Write the following equations in the form ax2 + bx + c = 0, and give the value of a, b, and c.

1. X2 = 6x

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2. 2x2 = 32

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3. 3x2 = 5x – 1

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4. 10 = 3x – x2

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5. (x + 2)2 = 9

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6. 4x2 = 64

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7.1x+x=5

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8. x (x−3)−1=0

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9. 8x = x2

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10.( 1x )2 = 6

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11. (x−3)2x=0

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12.x2 = 32

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13.x =1x+2

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14.x2 + 43=2x

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15.(x + 1)(x-3) = 6

A. Define each of the following terms.

1. Quadratic equation

2. Standard form of a quadratic equation

3. Real numbers

B. Which of the following equations are quadratic?

4. 4x = 2x2 – 6

5. 3x = 1

6. 5x2 = 30

7. 3x – 2 = 2x + 6

8. 2x – 5y = 0

9. 4x + 2x2 – 3x3 = 0

10. 12x2 – x = 11

C. Write the following equations in the form ax2 + bx + c = 0, and give the values of

a, b and c.

1. 3x2 = 6x

2. 3x2 = 32

3. 2x2 = 5x – 1

4. 12 = 4x – x2

5. (x + 3)2 = 8

6. 4x2 = 56

7. 1/x + x = 6

8. x(x – 4) – 1 = 0

9. 9x = x2

10. (1/x)2 = 10