Quadratics and inequalities

8 to solve 2 x x 2 0 by the quadratic formula let a 1

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8. To solve 2 x x 2 0 by the quadratic formula, let a 1, b 2, and c 0. 9. Two numbers that have a sum of 6 can be represented by x and x 6. 10. Some quadratic equations have one real and one imaginary solution. e e 2 4 df 2 d dug22241_ch10a.qxd 11/10/2004 18:30 Page 635
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636 Chapter 10 Quadratic Equations and Inequalities 10-20 10.2 Exercises Boost your GRADE at mathzone.com! Practice Problems Self-Tests Videos Reading and Writing After reading this section, write out the answers to these questions. Use complete sentences. 1. What is the quadratic formula used for? 2. When do you use the even-root property to solve a quadratic equation? 3. When do you use factoring to solve a quadratic equation? 4. When do you use the quadratic formula to solve a quadratic equation? 5. What is the discriminant? 6. How many solutions are there to any quadratic equation in the complex number system? Solve each equation by using the quadratic formula. See Example 1. 7. x 2 5 x 6 0 8. x 2 7 x 12 0 9. y 2 y 6 10. m 2 2 m 8 11. 6 z 2 7 z 3 0 12. 8 q 2 2 q 1 0 Solve each equation by using the quadratic formula. See Example 2. 13. 4 x 2 4 x 1 0 14. 4 x 2 12 x 9 0 15. 9 x 2 6 x 1 0 16. 9 x 2 24 x 16 0 17. 9 24 x 16 x 2 0 18. 4 20 x 25 x 2 Solve each equation by using the quadratic formula. See Example 3. 19. v 2 8 v 6 0 20. p 2 6 p 4 0 21. x 2 5 x 1 0 22. x 2 3 x 5 0 23. 2 t 2 6 t 1 0 24. 3 z 2 8 z 2 0 Solve each equation by using the quadratic formula. See Example 4. 25. 2 t 2 6 t 5 0 26. 2 y 2 1 2 y 27. 2 x 2 3 x 6 28. 3 x 2 2 x 5 0 29. 1 2 x 2 13 5 x 30. 1 4 x 2 1 4 7 2 x Find b 2 4 ac and the number of real solutions to each equation. See Example 5. 31. x 2 6 x 2 0 32. x 2 6 x 9 0 33. 2 x 2 5 x 6 0 34. x 2 3 x 4 0 35. 4 m 2 25 20 m 36. v 2 3 v 5 37. y 2 1 2 y 1 4 0 38. 1 2 w 2 1 3 w 1 4 0 39. 3 t 2 5 t 6 0 40. 9 m 2 16 24 m 41. 9 24 z 16 z 2 0 42. 12 7 x x 2 0 43. 5 x 2 7 0 44. 6 x 2 5 0 45. x 2 x 46. 3 x 2 7 x 0 Solve each equation by the method of your choice. 47. 1 4 y 2 y 1 48. 1 2 x 2 x 1 49. 1 3 x 2 1 2 x 1 3 50. 4 9 w 2 1 5 3 w Net Tutor e-Professors dug22241_ch10a.qxd 11/10/2004 18:30 Page 636
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10-21 10.2 The Quadratic Formula 637 51. 3 y 2 2 y 4 0 52. 2 y 2 3 y 6 0 53. w w 2 w w 3 54. 3 y y 4 y 2 4 55. 9(3 x 4 5) 2 1 56. 25(2 x 9 1) 2 0 57. 25 1 3 x 2 0 58. 4 2 9 1 4 x 2 0 59. 1 2 x 0 2 8 x 60. 3 x 4 2 6 x 1 61. ( x 8)( x 4) 42 62. ( x 10)( x 2) 20 63. y 3 8 ( ( 2 y y 1 5 ) ) 64. z 12 7 ( z z 4 1) Use the quadratic formula and a calculator to solve each equation. Round answers to three decimal places and check your answers. 65. x 2 3.2 x 5.7 0 66. x 2 7.15 x 3.24 0 67. x 2 7.4 x 13.69 0 68. 1.44 x 2 5.52 x 5.29 0 69. 1.85 x 2 6.72 x 3.6 0 70. 3.67 x 2 4.35 x 2.13 0 71. 3 x 2 14,379 x 243 0 72. x 2 12,347 x 6741 0 73. x 2 0.00075 x 0.0062 0 74. 4.3 x 2 9.86 x 3.75 0 Find the exact solution(s) to each problem. If the solution(s) are irrational, then also find approximate solution(s) to the nearest tenth. See Example 6. 75. Missing numbers. Find two positive real numbers that differ by 1 and have a product of 16. 76. Missing numbers. Find two positive real numbers that differ by 2 and have a product of 10.
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