008 chapter i

Chapter I 742950327660 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: ,[object Object]

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. 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. 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 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 -495300-779144Name: ___________________ 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. ,[object Object], _____________________________________________ ,[object Object], _____________________________________________ ,[object Object], _____________________________________________ ,[object Object], _____________________________________________ ,[object Object], _____________________________________________ ,[object Object], _____________________________________________ ,[object Object], _____________________________________________ ,[object Object], _____________________________________________ ,[object Object], _____________________________________________ ,[object Object], _____________________________________________ ,[object Object], _____________________________________________ ,[object Object], _____________________________________________ ,[object Object], _____________________________________________ ,[object Object], _____________________________________________ ,[object Object],Define each of the following terms. Quadratic equation Standard form of a quadratic equation Real numbers Which of the following equations are quadratic? 4x = 2x2 – 6 3x = 1 5x2 = 30 3x – 2 = 2x + 6 2x – 5y = 0 4x + 2x2 – 3x3 = 0 12x2 – x = 11 Write the following equations in the form ax2 + bx + c = 0, and give the values of a, b and c. 3x2 = 6x 3x2 = 32 2x2 = 5x – 1 12 = 4x – x2 (x + 3)2 = 8 4x2 = 56 1/x + x = 6 x(x – 4) – 1 = 0 9x = x2 10. (1/x)2 = 10

008 chapter i

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008 chapter i