Exercises 15.3, page 435

  1. 1. No more than two positive roots and three negative roots

  2. 3.  − 4 ,   − 2 ,  1

  3. 5.  − 3 ,   − 1 ,  2

  4. 7. 0.1 ,  16 ( − 3 + j15) ,  16 ( − 3 − j15)

  5. 9.  − 1 ,  12 ,  2

  6. 11.  − 2 ,   − 2 ,  2 ± 3

  7. 13.  − 2 ,  25 ,  1 + j3 ,  1 − j3

  8. 15.  − 3 ,   − 23 ,   − 12 ,  12

  9. 17.  − 3 ,   − 1 ,   − 1 ,  2 ,  2

  10. 19.

    2 ,  2 ,  2 ,  12j ,   − 12j

  11. 21.  − 2.17 ,  0.39 ,  1.78

  12. 23.  − 3.01 ,   − 1.49 ,   − 0.33 ,  0.33

  13. 25. x =  − 2 ,  y =  − 28 ;  x = 2 + 3 ,  y = 20 + 123 : x = 2 − 3 ,  y = 20 − 123

  14. 27.  − 34 ,  5 ,   − 5

  15. 29. x = 12 ,  x = 8

  16. 31. 1.8 s, 4.5 s

  17. 33. 0, L

  18. 35. 19.5%

  19. 37. 1.23 cm or 2.14 cm

  20. 39. 3.0 mm, 4.0 mm; 5.0 mm, 6.0 mm

  21. 41. (4 ,   − 7)

  22. 43. Two positive, one negative; zero positive, one negative, two nonreal complex

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