0013 chapter vi

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0013 chapter vi

  1. 1. Chapter VI<br />1049274248412<br /> <br />In this chapter, students will be taught how to find solutions to quadratic equations. This lesson assumes students are already familiar with solving simple quadratic equations by hand, and that they have become relatively comfortable using their graphing calculator for solving arithmetic problems and simple algebra problems. Students will also be shown strategies on how to use the keys on the graphing calculator to show a complete graph.<br />TARGET SKILLS:<br />At the end of this chapter, students are expected to:<br />• use calculator in solving quadratic equation; <br />• solve equation on a calculator; and.<br />• improve skills using calculator by solving quadratic equation.<br />Lesson 15<br />Equation on a Calculator<br /> OBJECTIVES:<br />At the end of this lesson, students are expected to:<br /><ul><li>acquire knowledge using calculator in solving quadratic equation;
  2. 2. resolve equations on a calculator; and
  3. 3. improve skills on solving quadratic equation using a calculator.</li></ul>The simplest way to solve a quadratic equation on a calculator is to use the quadratic formula.<br />X=-b ± d where d=b² - 4ac<br /> 2a<br />As we have seen, if d < 0, there are no real solutions. But f d ≥ 0, then we can use calculator to get the solutions.<br />To solve 3x² + 5x – 7 = 0, first compute the discriminant.<br />d = b² - 4ac = 5² - 4(3)(-7).<br />On an arithmetic calculator, the keystroke sequence for d is,<br />[AC][MC] 4 [x] 3 [x] 7 [=][M+] 5 [x][=][+][MR][=]<br />The display will show the value of the discriminant to be 109, and so the quadratic equation has two distinct roots. To compute the roots, proceed as follows:<br />[AC][MC] 109 [√][M+][MR][-] 5 [+] 2 [x] 3 [=] the first root and <br />0 [-][MR][-] 5 [+] 2 [ x] 3 [=] the second root.<br />On an algebraic calculator, the keystroke sequence is easier. Recall that the actual roots are:<br />x= -5 + 5² - 4(3)(-7) <br /> 2(3)<br />x= -5 - 5² - 4(3)(-7) <br /> 2(3)<br />First, we compute the square root of the discriminant and store it is memory.<br />[AC] 5 [2] – 4 [x] 3 [x] 7 [+/-][=][√][Min]<br />Then, compute the first root as:<br />x1 = (5 [+/-][+][MR])[÷] (2 [x] 3) [=];<br />and then compute the second root as:<br />x2 = (5[+/-][-][MR])[+] (2 [x] 3)[=].<br />Exercise: <br />Find the roots of the following equations.<br /><ul><li>3.5x2 + 1.2x – 3.2 = 0
  4. 4. 7.6 -2.2x – 1.7x2 = 0
  5. 5. 2.5x2 + 5.6x – 13.5 = 0
  6. 6. x – 77.3 + 2.3x2 = 0
  7. 7. x2 - 1000.5 + 32.3 = 0</li></ul>-391885-605427Name: ___________________ Section: _______<br />Instructor: ________________ Date: _______ Rating: ____<br /> <br /> <br /> Instruction: Find the roots o the following equations.<br /><ul><li>5.3x2 + 2.1v – 2.3 = 0
  8. 8. _____________________________________________________
  9. 9. 6.7 v - 2.2x – 7.1x2 = 0
  10. 10. _____________________________________________________
  11. 11. 5.2x2 + 6.5x – 5.13 = 0
  12. 12. _____________________________________________________
  13. 13. x2 – 50.001 + 33.2 = 0
  14. 14. _____________________________________________________
  15. 15. x – 7.73 + 2.3x2 = 0
  16. 16. ____________________________________________________
  17. 17. 3.3x2 – 1.9x – 7.10 = 0
  18. 18. -392430-469900_____________________________________________________
  19. 19. 3.1x – 9.1x2 – 7.10 = 0
  20. 20. _____________________________________________________
  21. 21. 6.3x2+ 8.5x = 9.5
  22. 22. _____________________________________________________
  23. 23. 5.9x – 9.5x2 = 8.03
  24. 24. _____________________________________________________
  25. 25. 3.2x2 + 2.3x = 23.32
  26. 26. _____________________________________________________
  27. 27. 9.9x – 7.7x2 – 8.8 = 0
  28. 28. _____________________________________________________
  29. 29. 6.3x + 5.3x2 – 3.4 = 0
  30. 30. _____________________________________________________
  31. 31. 6.3x2 – 2.9x – 8.10 = 0
  32. 32. _____________________________________________________
  33. 33. 3.4x – 8.1x2 – 4.10 = 0
  34. 34. _____________________________________________________
  35. 35. 6.2x2 + 3.6v – 3.7 = 0</li></ul> <br />Instruction: Find the roots o the following equations.<br /><ul><li>5.3f2 + 2.1f – 2.4 = 0
  36. 36. 6.7 x - 2.2x – 8.1x2 = 0
  37. 37. 5.2r2 + 6.5r – 5.13 = 0
  38. 38. s2 – 50.001 + 33.2 = 0
  39. 39. g – 7.73 + 2.3g2 = 0
  40. 40. 3.3o2 – 1.9o – 7.10 = 0
  41. 41. 3.1e – 9.1e2 – 7.10 = 0
  42. 42. 6.3r2+ 8.5r = 9.5
  43. 43. 5.9i – 9.5i2 = 8.03
  44. 44. 3.2o2 + 2.3o = 23.32
  45. 45. 9.9p – 7.7p2 – 8.8 = 0
  46. 46. 6.3h + 5.3h2 – 3.8 = 0
  47. 47. 6.3x2 – 3.9x – 8.10 = 0
  48. 48. 3.4x – 9.1x2 – 4.10 = 0
  49. 49. 5.2v2 + 3.6v – 4.7 = 0

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