Chapter 4
Section 4.1: Solving Quadratics by Factoring
1. $6,\ \ -1$ 3. $7,\ \ -3$ 5. $2,\ \ -5$ 7. $0,\ \ 8$ 9. $-3,\ \ -1$
11. $-1,\ \ -{\scriptstyle{}^{2}\!\!\diagup\!\!{}_{3}\;}$ 13. 1, $-{\scriptstyle{}^{1}\!\!\diagup\!\!{}_{2}\;}$ 15. ${\scriptstyle{}^{1}\!\!\diagup\!\!{}_{3}\;},\ \ {\scriptstyle{}^{1}\!\!\diagup\!\!{}_{4}\;}$ 17. $-6,\ \ -1$ 19. $-1$, 6
21. $-3,\ \ -{\scriptstyle{}^{5}\!\!\diagup\!\!{}_{2}\;}$ 23. $4a,\ \ -a$ 25. $4a,\ \ -3a$
Section 4.2: Completing the Square
1. $3\pm \sqrt{3}$ 3. 2 5. 18, 2 7. $-7\pm 2\sqrt{13}$ 9. $9\pm \sqrt{94}$
11. $-3\pm \sqrt{7}$ 13. $12\pm \sqrt{141}$ 15. $4,\ \ -2$ 17. $-11,\ \ -1$ 19. 0, 6
21. $-3\pm \sqrt{47}$ 23. $7\pm \sqrt{19}$ 25. $2\pm \sqrt{31}$ 27. $-8,\ \ 2$
Section 4.3: The Quadratic Formula
1. $\tfrac{-5\pm \sqrt{37}}{2}$ 3. $-1,\ \ {\scriptstyle{}^{1}\!\!\diagup\!\!{}_{2}\;}$ 5. $\tfrac{-5\pm \sqrt{33}}{4}$ 7. No sol'ns. 9. $\tfrac{5\pm \sqrt{13}}{4}$
11. $\pm \tfrac{\sqrt{6}}{2}$ 13. $\tfrac{7\pm 3\sqrt{5}}{2}$ 15. No sol'ns. 17. $3\pm \sqrt{11}$ 19. $-3,\ \ 1$
21. $1,\ \ -7$ 23. ${\scriptstyle{}^{5}\!\!\diagup\!\!{}_{2}\;},\ \ {\scriptstyle{}^{1}\!\!\diagup\!\!{}_{2}\;}$ 25. ${\scriptstyle{}^{2}\!\!\diagup\!\!{}_{3}\;},\ \ -{\scriptstyle{}^{1}\!\!\diagup\!\!{}_{2}\;}$ 27. $3\pm \sqrt{7}$ 29. ${\scriptstyle{}^{1}\!\!\diagup\!\!{}_{2}\;},\ \ -{\scriptstyle{}^{7}\!\!\diagup\!\!{}_{2}\;}$
31. $\tfrac{1\pm \sqrt{5}}{2}$ 33. $\tfrac{-13\pm \sqrt{69}}{2}$ 35. $1\pm \sqrt{26}$ 37. $\tfrac{-17\pm \sqrt{689}}{2}$
Section 4.4: Quadratic Equations from Fractions
1. $0,\ \ -1$ 3. 5, 6 5. $3,~-\tfrac{14}{3}$ 7. $\tfrac{13\pm \sqrt{37}}{6}$ 9. ${\scriptstyle{}^{1}\!\!\diagup\!\!{}_{3}\;},\ \ 2$
11. ${\scriptstyle{}^{1}\!\!\diagup\!\!{}_{2}\;}$ 13. $18,\ \ -2$ 15. $-5$ 17. $-32$ 19. 4
21. $5\pm \sqrt{13}$ 23. $-2,\ \ -3$ 25. $\tfrac{9\pm 5\sqrt{5}}{2}$
Section 4.5: Quadratic Word Problems
1. 5 and 10 or –10 and –5 3. 5 and 6 or –6 and –5 5. 6 and 8
7. a. First time: $\tfrac{3}{5}$ sec. b. 35 meters 9. 8 and 12 11. 65
13. 304, 340, 430, 403, 500 15. $\tfrac{1}{2}$inch 17. Jack: 3 mph; Jill: 5 mph.
19. 60 mph 21. 6 by 9 23. $\tfrac{-5+\sqrt{265}}{2}$ by $\tfrac{5+\sqrt{265}}{2}$
25. 18, 19, 20 or $-23$, $-22$, $-21$ 27. 40 mph
Section 4.6: The Discriminant
1. $D=289={{17}^{2}}$ 2 rational solutions 3. $D=0={{0}^{2}}$ 1 rational solution 5. $D=1={{1}^{2}}$ 2 rational solutions
7. $D=29$ 2 irrational solutions 9. $D=-11$ No solutions 11. $D=0={{0}^{2}}$ 1 rational solution
13. 16 15. $\pm 2\sqrt{6}$ 17. $\pm 20\sqrt{3}$
Section 4.7: Miscellaneous Quadratic Equation Problems
1. $5,\ \ -2$ 3. $3,\ \ -4$ 5. $4,\ \ -9$ 7. $\tfrac{5\pm \sqrt{73}}{4}$ 9. $2\pm \sqrt{5}$ 11. ${\scriptstyle{}^{1}\!\!\diagup\!\!{}_{2}\;}$
13. $\tfrac{-9\pm \sqrt{89}}{2}$ 15. $2,\ \ -3$ 17. 0, 8 19. $8,\ \ -1$ 21. $\tfrac{1\pm \sqrt{3}}{2}$ 23. $5\pm 2\sqrt{3}$
25. 5, 6 27. 3, 4 29. $-{\scriptstyle{}^{22}\!\!\diagup\!\!{}_{3}\;}$ 31. $11,\ \ -7$ 33. $\pm 4$
35. No Sol'ns. 37. $\pm {\scriptstyle{}^{9}\!\!\diagup\!\!{}_{7}\;}$ 39. $\tfrac{-1\pm \sqrt{146}}{5}$ 41. $\pm 2,\ \ \pm 3$ 43. $\pm \sqrt{2},\ \ \pm \sqrt{3}$
45. $3a,\ \ -a$ 47. $\tfrac{a\pm a\sqrt{97}}{4}$ 49. $\tfrac{-1\pm \sqrt{37}}{3}$ 51. $b\pm b\sqrt{3}$ 53. $\tfrac{-3\pm \sqrt{17}}{2K}$