A-19 Answers to Selected Exercises 14. (a) Positive Negative Nonreal Complex 0 4 0 0 2 2 0 0 4 x y 20 –1 0 1 f(x) = –2x4 – x3 + x + 2 Positive Negative Nonreal Complex 1 3 0 1 1 2 Positive Negative Nonreal Complex 2 2 0 2 0 2 0 2 2 0 0 4 x y 400 –500 –3 2 0 5 f(x) = 2x5 – 10x4 + x3 – 5x2 – x + 5 Positive Negative Nonreal Complex 4 1 0 2 1 2 0 1 4 13. (a) (b) {1, {5, { 1 2, { 5 2 (c) 5 (d) - 22 2 , 22 2 (e) -i, i (f) Q- 22 2 , 0R , Q 22 2 , 0R , 15, 02 (g) 10, 52 (h) ƒ142 = -527; 14, -5272 (i) (j) (b) {1, {2, {3, {6, {9, {18, { 1 3, { 2 3 (c) - 2 3 , 3 (d) -1 + 213 2 , -1 - 213 2 (e) no other complex zeros (f) A - 2 3 , 0B, 13, 02, Q -1 { 213 2 , 0R (g) 10, 182 15. (a) (b) {1, {2, { 1 2 (c) -1, 1 (d) no other real zeros (e) - 1 4 + 215 4 i , - 1 4 - 215 4 i (f) 1-1, 02, 11, 02 (g) 10, 22 (h) ƒ142 = -570; 14, -5702 (i) (j) 16. (a) (h) ƒ142 = 238; 14, 2382 (i) (j) x y 15 –30 –3 0 5 2 f(x) = 3x4 – 4x3 – 22x2 + 15x + 18 16. (b) 0, {1, {3, {9, {27, { 1 2 , { 3 2 , { 9 2 , { 27 2 , { 1 4 , { 3 4 , { 9 4 , { 27 4 (c) 0, - 3 2 (multiplicity 2) (d) no other real zeros (e) 1 2 + 211 2 i, 1 2 - 211 2 i (f) A - 3 2, 0B , 10, 02 (g) 10, 02 (h) ƒ142 = 7260; 14, 72602 (i) (j) x y 20 –20 0 3 2 – f(x) = 4x5 + 8x4 + 9x3 + 27x2 + 27x 17. (a) Positive Negative Nonreal Complex 1 1 2 x y 20 0 –30 –Î5 Î5 f(x) = 3x4 – 14x2 – 5 (b) {1, {5, { 1 3 , { 5 3 (c) no rational zeros (d) -25, 25 (e) - 23 3 i, 23 3 i (f) A -25, 0B , A 25, 0B (g) 10, -52 (h) ƒ142 = 539; 14, 5392 (i) (j) Positive Negative Nonreal Complex 4 0 0 2 0 2 0 0 4 Positive Negative Nonreal Complex 2 3 0 2 1 2 0 3 2 0 1 4 18. (a) (b) {1, {3, {9 (c) -3, -1 (multiplicity 2), 1, 3 (d) no other real zeros (e) no other complex zeros (f) 1-3, 02, 1-1, 02, 11, 02, 13, 02 (g) 10, -92 (h) ƒ142 = -525; 14, -5252 (i) (j) x y –3 –1 1 3 40 f(x) = –x5 – x4 + 10x3 + 10x2 – 9x – 9 0 19. (a) (b) {1, {2, {3, {4, {6, {12, { 1 3 , { 2 3 , { 4 3 (c) 1 3 , 2 (multiplicity 2), 3 (d) no other real zeros (e) no other complex zeros (f) A1 3 , 0B , 12, 02, 13, 02 (g) 10, -122 (h) ƒ142 = -44; 14, -442 (i)
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