008 chapter i

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008 chapter i

  1. 1. Chapter I<br />742950327660<br />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.<br />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.<br />Lesson 1<br />Identifying the quadratic equation<br /> OBJECTIVES:<br />At the end of this lesson, students are expected to:<br /><ul><li>define the quadratic equation;
  2. 2. discuss real numbers in quadratic equation; and
  3. 3. improve writing the standard form of the quadratic equation.</li></ul>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.<br />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.<br />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.<br />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.<br />Example A. Express x2 = 8x in standard form<br /> x2 = 8x can be written as x2 - 8x = 0<br /> where a=1, b= ˉ8, and c=0.<br />Example B. Express x2 = 64 in standard form<br /> x2 = 64 can be written as x2 – 64 = 0<br /> where a=1. B=0, and c=ˉ64.<br />Example C. Express the fractional equation x = 1/x-3 as a quadratic equation.<br /> x = 1/x-3 <br /> x (x-3) = 1 multiply both sides by x-3<br /> x² - 3x = 1 using the distributive property<br /> x² - 3x - 1 = 0 a=1, b=ˉ3, c=ˉ1<br />Exercises: <br />Which of the following equations are quadratic?<br />1. 3x = x² - 5<br />2. 2x =1<br />3. x² = 25<br />4. 2x - 3 = x + 5<br />5. 5x – 2y = 0<br />-495300-779144Name: ___________________ Section: _______<br />Instructor: ________________ Date: _______ Rating: ____<br /> <br />Instruction: Write the following equations in the form ax2 + bx + c = 0, and give the value of a, b, and c.<br /><ul><li>X2 = 6x</li></ul> _____________________________________________<br /><ul><li>2x2 = 32</li></ul> _____________________________________________ <br /><ul><li>3x2 = 5x – 1 </li></ul> _____________________________________________<br /><ul><li>10 = 3x – x2</li></ul> _____________________________________________<br /><ul><li>(x + 2)2 = 9</li></ul> _____________________________________________<br /><ul><li>4x2 = 64</li></ul> _____________________________________________<br /><ul><li>-514350-7219371x+ x =5 </li></ul> _____________________________________________<br /><ul><li>x(x-3)-1=0</li></ul> _____________________________________________<br /><ul><li>8x = x2</li></ul> _____________________________________________<br /><ul><li> 1x2 = 6</li></ul> _____________________________________________<br /><ul><li>(x-3)2x=0</li></ul> _____________________________________________<br /><ul><li>x2 = 32</li></ul> _____________________________________________<br /><ul><li>x =1x+2</li></ul> _____________________________________________ <br /><ul><li>x2 + 43 = 2x</li></ul> _____________________________________________<br /><ul><li>(x + 1)(x-3) = 6</li></ul>Define each of the following terms.<br />Quadratic equation<br />Standard form of a quadratic equation<br />Real numbers<br />Which of the following equations are quadratic?<br />4x = 2x2 – 6<br />3x = 1<br />5x2 = 30 <br />3x – 2 = 2x + 6<br />2x – 5y = 0<br />4x + 2x2 – 3x3 = 0<br /> 12x2 – x = 11<br />Write the following equations in the form ax2 + bx + c = 0, and give the values of a, b and c.<br />3x2 = 6x<br />3x2 = 32<br />2x2 = 5x – 1<br />12 = 4x – x2 <br />(x + 3)2 = 8<br />4x2 = 56<br />1/x + x = 6<br />x(x – 4) – 1 = 0<br />9x = x2 <br />10. (1/x)2 = 10<br />

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