Exercises 15.3, page 435

1. No more than two positive roots and three negative roots
3. $- 4, - 2, 1$ $- 4, - 2, 1$
5. $- 3, - 1, 2$ $- 3, - 1, 2$
7. $0.1, \frac{1}{6} (- 3 + j \sqrt{15}), \frac{1}{6} (- 3 - j \sqrt{15})$ $0.1, \frac{1}{6} (- 3 + j \sqrt{15}), \frac{1}{6} (- 3 - j \sqrt{15})$
9. $- 1, \frac{1}{2}, 2$ $- 1, \frac{1}{2}, 2$
11. $- 2, - 2, 2 \pm \sqrt{3}$ $- 2, - 2, 2 \pm \sqrt{3}$
13. $- 2, \frac{2}{5}, 1 + j \sqrt{3}, 1 - j \sqrt{3}$ $- 2, \frac{2}{5}, 1 + j \sqrt{3}, 1 - j \sqrt{3}$
15. $- 3, - \frac{2}{3}, - \frac{1}{2}, \frac{1}{2}$ $- 3, - \frac{2}{3}, - \frac{1}{2}, \frac{1}{2}$
17. $- 3, - 1, - 1, 2, 2$ $- 3, - 1, - 1, 2, 2$
19.

$2, 2, 2, \frac{1}{2} j, - \frac{1}{2} j \frac{}{}$ $2, 2, 2, \frac{1}{2} j, - \frac{1}{2} j \frac{}{}$
21. $- 2.17, 0.39, 1.78$ $- 2.17, 0.39, 1.78$
23. $- 3.01, - 1.49, - 0.33, 0.33$ $- 3.01, - 1.49, - 0.33, 0.33$
25. $\begin{array}{l} x = - 2, y = - 28; x = 2 + \sqrt{3}, y = 20 + 12 \sqrt{3} : \\ x = 2 - \sqrt{3}, y = 20 - 12 \sqrt{3} \end{array}$ $\begin{array}{l} x = - 2, y = - 28; x = 2 + \sqrt{3}, y = 20 + 12 \sqrt{3} : \\ x = 2 - \sqrt{3}, y = 20 - 12 \sqrt{3} \end{array}$
27. $- \frac{3}{4}, \sqrt{5}, - \sqrt{5}$ $- \frac{3}{4}, \sqrt{5}, - \sqrt{5}$
29. $x = \frac{1}{2}, x = 8$ $x = \frac{1}{2}, x = 8$
31. 1.8 s, 4.5 s
33. 0, L
35. 19.5%
37. 1.23 cm or 2.14 cm
39. 3.0 mm, 4.0 mm; 5.0 mm, 6.0 mm
41. $(4, - 7)$ $(4, - 7)$
43. Two positive, one negative; zero positive, one negative, two nonreal complex

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Table of Contents for Exercises 15.3, page 435