Explanation Given Information: The provided polynomial equation is x 3 − 1 = 0 . Formula used: Zero product rule: An equation a b = 0 is true if and only if a = 0 or b = 0 , both A product is zero if and only if at least one factor is zero The value of x in the equation a x 2 + b x + c = 0 can be given by the quadratic formula, x = − b ± b 2 − 4 a c 2 a where a , b and c are real numbers with a ≠ 0 . Calculation: Consider the polynomial equation x 3 − 1 = 0 . First determine the single solution in this cubic equation x 3 − 1 = 0 Compare the equation x 3 − 1 = 0 with the standard cubic equation a x 3 + b x 2 + c x + d = 0 . a = 1 and d = − 1 Therefore, possible factor of 1 is x = ± 1 and − 1 is x = ± 1 First try x = 1 substitute in the provided polynomial equation x 3 − 1 = 0 , ( 1 ) 3 − 1 = ? 0 1 − 1 = ? 0 0 = 0 This is true Therefore, x − 1 is a factor of the polynomial x 3 − 1 = 0 . In order to find other two values of x , divide x 3 − 1 = 0 by x − 1 , x − 1 x 2 + x + 1 x 3 + 0 x 2 + 0 x − 1 x 3 − x 2 _ x 2 + 0 x x 2 − x _ �

Student Solutions Manual for Waner/Costenoble's Finite Math and Applied Calculus, 7th

7th Edition

ISBN: 9781337275972

Author: Waner, Stefan; Costenoble, Steven

Publisher: Cengage Learning

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Chapter 0.5, Problem 35E

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Chapter 0.5, Problem 34E

Chapter 0.5, Problem 36E

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For Exercises 31–56, perform the indicated operations. Write the answers in standard form, a + bi. (See Examples 3-6) 31. (2 – 7i) + (8 – 3i) 32. (6 – 10i) + (8 + 4i) 33. (15 + 21i) – (18 – 40i) 34. (250 + 100i) – (80 + 25i) 35. (2.3 + 4i) – (8.1 – 2.7i) + (4.6 – 6.7i) 36. (0.05 – 0.03i) + (-0.12 + 0.08i) – (0.07 + 0.05i) 37. 2i(5 + i) 38. 4i(6 + 5i) 39. (3 – 6i)(10 + i) 40. (2 – 5i)(8 + 2i) 43. (3 – V-5)(4 + V-5) 46. (3 – 21)? + (3 + 2i)? 41. (3 - 42. (10 — З1)? 44. (2 + V=7)(10 + V-7) 45. (2 – i)? + (2 + i)? 47. (10 – 4i)(10 + 4i) 48. (3 9i)(3 + 9i) 49. (V2 + V3i)(V2 - V3i) 50. (V3 + V7i)(V5 – Vīi) 6 + 2i 51. 3 - i 5 + i 52. 4 - i 8 - 5i 53. 13 + 2i 10 – 3i 54. 11 + 4i 55. 13i 56. 7i

Exercise 6.3.3 Find the four fourth roots of 16.

Chapter 0 Solutions

Student Solutions Manual for Waner/Costenoble's Finite Math and Applied Calculus, 7th

Ch. 0.1 - Prob. 1E Ch. 0.1 - Prob. 2E Ch. 0.1 - Prob. 3E Ch. 0.1 - Prob. 4E Ch. 0.1 - Prob. 5E Ch. 0.1 - Prob. 6E Ch. 0.1 - Prob. 7E Ch. 0.1 - Prob. 8E Ch. 0.1 - Prob. 9E Ch. 0.1 - Prob. 10E

Ch. 0.1 - Prob. 11E Ch. 0.1 - Prob. 12E Ch. 0.1 - Prob. 13E Ch. 0.1 - Prob. 14E Ch. 0.1 - Prob. 15E Ch. 0.1 - Prob. 16E Ch. 0.1 - Calculate each expression in Exercises 124, giving...Ch. 0.1 - Prob. 18E Ch. 0.1 - Prob. 19E Ch. 0.1 - Prob. 20E Ch. 0.1 - Prob. 21E Ch. 0.1 - Prob. 22E Ch. 0.1 - Prob. 23E Ch. 0.1 - Prob. 24E Ch. 0.1 - Prob. 25E Ch. 0.1 - Prob. 26E Ch. 0.1 - Prob. 27E Ch. 0.1 - Prob. 28E Ch. 0.1 - Prob. 29E Ch. 0.1 - Prob. 30E Ch. 0.1 - Prob. 31E Ch. 0.1 - Prob. 32E Ch. 0.1 - Prob. 33E Ch. 0.1 - Prob. 34E Ch. 0.1 - Prob. 35E Ch. 0.1 - Prob. 36E Ch. 0.1 - Convert each expression in Exercises 25-50 into...Ch. 0.1 - Convert each expression in Exercises 25-50 into...Ch. 0.1 - Prob. 39E Ch. 0.1 - Prob. 40E Ch. 0.1 - Prob. 41E Ch. 0.1 - Prob. 42E Ch. 0.1 - Prob. 43E Ch. 0.1 - Prob. 44E Ch. 0.1 - Prob. 45E Ch. 0.1 - Prob. 46E Ch. 0.1 - Prob. 47E Ch. 0.1 - Prob. 48E Ch. 0.1 - Prob. 49E Ch. 0.1 - Prob. 50E Ch. 0.2 - Evaluate the expression sin Exercises 116. 33 Ch. 0.2 - Evaluate the expression sin Exercises 116. (2)3 Ch. 0.2 - Prob. 3E Ch. 0.2 - Prob. 4E Ch. 0.2 - Prob. 5E Ch. 0.2 - Prob. 6E Ch. 0.2 - Prob. 7E Ch. 0.2 - Prob. 8E Ch. 0.2 - Prob. 9E Ch. 0.2 - Prob. 10E Ch. 0.2 - Prob. 11E Ch. 0.2 - Prob. 12E Ch. 0.2 - Prob. 13E Ch. 0.2 - Prob. 14E Ch. 0.2 - Prob. 15E Ch. 0.2 - Prob. 16E Ch. 0.2 - Prob. 17E Ch. 0.2 - Prob. 18E Ch. 0.2 - Prob. 19E Ch. 0.2 - Prob. 20E Ch. 0.2 - Prob. 21E Ch. 0.2 - Prob. 22E Ch. 0.2 - Prob. 23E Ch. 0.2 - Prob. 24E Ch. 0.2 - Prob. 25E Ch. 0.2 - Prob. 26E Ch. 0.2 - Prob. 27E Ch. 0.2 - Prob. 28E Ch. 0.2 - Prob. 29E Ch. 0.2 - Prob. 30E Ch. 0.2 - Prob. 31E Ch. 0.2 - Prob. 32E Ch. 0.2 - Convert the expressions in Exercises 31-36 to...Ch. 0.2 - Prob. 34E Ch. 0.2 - Prob. 35E Ch. 0.2 - Prob. 36E Ch. 0.2 - Prob. 37E Ch. 0.2 - Prob. 38E Ch. 0.2 - Prob. 39E Ch. 0.2 - Prob. 40E Ch. 0.2 - Prob. 41E Ch. 0.2 - Prob. 42E Ch. 0.2 - Prob. 43E Ch. 0.2 - Prob. 44E Ch. 0.2 - Prob. 45E Ch. 0.2 - Prob. 46E Ch. 0.2 - Prob. 47E Ch. 0.2 - Prob. 48E Ch. 0.2 - Prob. 49E Ch. 0.2 - Prob. 50E Ch. 0.2 - Prob. 51E Ch. 0.2 - Prob. 52E Ch. 0.2 - Prob. 53E Ch. 0.2 - Prob. 54E Ch. 0.2 - Prob. 55E Ch. 0.2 - Prob. 56E Ch. 0.2 - Prob. 57E Ch. 0.2 - Prob. 58E Ch. 0.2 - Prob. 59E Ch. 0.2 - Prob. 60E Ch. 0.2 - Simplify the expressions in Exercises 5764, given...Ch. 0.2 - Prob. 62E Ch. 0.2 - Prob. 63E Ch. 0.2 - Prob. 64E Ch. 0.2 - Prob. 65E Ch. 0.2 - Prob. 66E Ch. 0.2 - Prob. 67E Ch. 0.2 - Prob. 68E Ch. 0.2 - Prob. 69E Ch. 0.2 - Prob. 70E Ch. 0.2 - Prob. 71E Ch. 0.2 - Prob. 72E Ch. 0.2 - Prob. 73E Ch. 0.2 - Prob. 74E Ch. 0.2 - Prob. 75E Ch. 0.2 - Prob. 76E Ch. 0.2 - Prob. 77E Ch. 0.2 - Prob. 78E Ch. 0.2 - Prob. 79E Ch. 0.2 - Prob. 80E Ch. 0.2 - Prob. 81E Ch. 0.2 - Prob. 82E Ch. 0.2 - Prob. 83E Ch. 0.2 - Prob. 84E Ch. 0.2 - Prob. 85E Ch. 0.2 - Prob. 86E Ch. 0.2 - Convert the expressions in Exercises 8596 radical...Ch. 0.2 - Prob. 88E Ch. 0.2 - Prob. 89E Ch. 0.2 - Prob. 90E Ch. 0.2 - Prob. 91E Ch. 0.2 - Prob. 92E Ch. 0.2 - Prob. 93E Ch. 0.2 - Prob. 94E Ch. 0.2 - Prob. 95E Ch. 0.2 - Prob. 96E Ch. 0.2 - Prob. 97E Ch. 0.2 - Prob. 98E Ch. 0.2 - Prob. 99E Ch. 0.2 - Prob. 100E Ch. 0.2 - Prob. 101E Ch. 0.2 - Prob. 102E Ch. 0.2 - Prob. 103E Ch. 0.2 - Prob. 104E Ch. 0.2 - Prob. 105E Ch. 0.2 - Prob. 106E Ch. 0.2 - Prob. 107E Ch. 0.2 - Prob. 108E Ch. 0.2 - Prob. 109E Ch. 0.2 - Prob. 110E Ch. 0.2 - Prob. 111E Ch. 0.2 - Prob. 112E Ch. 0.2 - Prob. 113E Ch. 0.2 - Prob. 114E Ch. 0.2 - Prob. 115E Ch. 0.2 - Prob. 116E Ch. 0.2 - Prob. 117E Ch. 0.2 - Prob. 118E Ch. 0.2 - Prob. 119E Ch. 0.2 - Prob. 120E Ch. 0.3 - Prob. 1E Ch. 0.3 - Prob. 2E Ch. 0.3 - Prob. 3E Ch. 0.3 - Prob. 4E Ch. 0.3 - Prob. 5E Ch. 0.3 - Prob. 6E Ch. 0.3 - Prob. 7E Ch. 0.3 - Prob. 8E Ch. 0.3 - Prob. 9E Ch. 0.3 - Prob. 10E Ch. 0.3 - Prob. 11E Ch. 0.3 - Expand each expression in Exercises 122. (y1y)2 Ch. 0.3 - Prob. 13E Ch. 0.3 - Prob. 14E Ch. 0.3 - Prob. 15E Ch. 0.3 - Prob. 16E Ch. 0.3 - Prob. 17E Ch. 0.3 - Prob. 18E Ch. 0.3 - Prob. 19E Ch. 0.3 - Prob. 20E Ch. 0.3 - Prob. 21E Ch. 0.3 - Prob. 22E Ch. 0.3 - Prob. 23E Ch. 0.3 - Prob. 24E Ch. 0.3 - Prob. 25E Ch. 0.3 - Prob. 26E Ch. 0.3 - Prob. 27E Ch. 0.3 - Prob. 28E Ch. 0.3 - Prob. 29E Ch. 0.3 - Prob. 30E Ch. 0.3 - Prob. 31E Ch. 0.3 - Prob. 32E Ch. 0.3 - Prob. 33E Ch. 0.3 - Prob. 34E Ch. 0.3 - Prob. 35E Ch. 0.3 - Prob. 36E Ch. 0.3 - Prob. 37E Ch. 0.3 - Prob. 38E Ch. 0.3 - Prob. 39E Ch. 0.3 - Prob. 40E Ch. 0.3 - Prob. 41E Ch. 0.3 - Prob. 42E Ch. 0.3 - Prob. 43E Ch. 0.3 - Prob. 44E Ch. 0.3 - Prob. 45E Ch. 0.3 - Prob. 46E Ch. 0.3 - Prob. 47E Ch. 0.3 - Prob. 48E Ch. 0.4 - Prob. 1E Ch. 0.4 - Prob. 2E Ch. 0.4 - Prob. 3E Ch. 0.4 - Prob. 4E Ch. 0.4 - Prob. 5E Ch. 0.4 - Prob. 6E Ch. 0.4 - Rewrite each expression in Exercises 116 as a...Ch. 0.4 - Prob. 8E Ch. 0.4 - Rewrite each expression in Exercises 116 as a...Ch. 0.4 - Prob. 10E Ch. 0.4 - Prob. 11E Ch. 0.4 - Prob. 12E Ch. 0.4 - Prob. 13E Ch. 0.4 - Rewrite each expression in Exercises 116 as a...Ch. 0.4 - Prob. 15E Ch. 0.4 - Prob. 16E Ch. 0.5 - Prob. 1E Ch. 0.5 - Prob. 2E Ch. 0.5 - Prob. 3E Ch. 0.5 - Prob. 4E Ch. 0.5 - Prob. 5E Ch. 0.5 - Prob. 6E Ch. 0.5 - Prob. 7E Ch. 0.5 - Prob. 8E Ch. 0.5 - Prob. 9E Ch. 0.5 - Prob. 10E Ch. 0.5 - Prob. 11E Ch. 0.5 - Prob. 12E Ch. 0.5 - Prob. 13E Ch. 0.5 - Prob. 14E Ch. 0.5 - Prob. 15E Ch. 0.5 - Prob. 16E Ch. 0.5 - Prob. 17E Ch. 0.5 - Prob. 18E Ch. 0.5 - Prob. 19E Ch. 0.5 - Prob. 20E Ch. 0.5 - Prob. 21E Ch. 0.5 - Prob. 22E Ch. 0.5 - Prob. 23E Ch. 0.5 - Prob. 24E Ch. 0.5 - Prob. 25E Ch. 0.5 - Prob. 26E Ch. 0.5 - Prob. 27E Ch. 0.5 - Prob. 28E Ch. 0.5 - Prob. 29E Ch. 0.5 - Prob. 30E Ch. 0.5 - Prob. 31E Ch. 0.5 - Prob. 32E Ch. 0.5 - Prob. 33E Ch. 0.5 - Find all possible real solutions of each equation...Ch. 0.5 - Prob. 35E Ch. 0.5 - Prob. 36E Ch. 0.5 - Prob. 37E Ch. 0.5 - Prob. 38E Ch. 0.5 - Prob. 39E Ch. 0.5 - Prob. 40E Ch. 0.5 - Prob. 41E Ch. 0.5 - Prob. 42E Ch. 0.5 - Prob. 43E Ch. 0.5 - Prob. 44E Ch. 0.6 - Prob. 1E Ch. 0.6 - Prob. 2E Ch. 0.6 - Prob. 3E Ch. 0.6 - Prob. 4E Ch. 0.6 - Prob. 5E Ch. 0.6 - Prob. 6E Ch. 0.6 - Prob. 7E Ch. 0.6 - Prob. 8E Ch. 0.6 - Prob. 9E Ch. 0.6 - Prob. 10E Ch. 0.6 - Prob. 11E Ch. 0.6 - Prob. 12E Ch. 0.6 - Prob. 13E Ch. 0.6 - Prob. 14E Ch. 0.6 - Prob. 15E Ch. 0.6 - Prob. 16E Ch. 0.6 - Prob. 17E Ch. 0.6 - Prob. 18E Ch. 0.6 - Prob. 19E Ch. 0.6 - Prob. 20E Ch. 0.6 - Prob. 21E Ch. 0.6 - Prob. 22E Ch. 0.6 - Prob. 23E Ch. 0.6 - Prob. 24E Ch. 0.6 - Prob. 25E Ch. 0.6 - Prob. 26E Ch. 0.7 - Prob. 1E Ch. 0.7 - Prob. 2E Ch. 0.7 - Prob. 3E Ch. 0.7 - Prob. 4E Ch. 0.7 - Prob. 5E Ch. 0.7 - Prob. 6E Ch. 0.7 - Prob. 7E Ch. 0.7 - Prob. 8E Ch. 0.7 - Prob. 9E Ch. 0.7 - Prob. 10E Ch. 0.7 - Prob. 11E Ch. 0.7 - Prob. 12E Ch. 0.7 - Prob. 13E Ch. 0.7 - Prob. 14E Ch. 0.7 - Prob. 15E Ch. 0.7 - Prob. 16E Ch. 0.7 - Prob. 17E Ch. 0.7 - Prob. 18E Ch. 0.7 - Prob. 19E Ch. 0.7 - Prob. 20E Ch. 0.8 - In Exercises 14, complete the given tables....Ch. 0.8 - Prob. 2E Ch. 0.8 - Prob. 3E Ch. 0.8 - Prob. 4E Ch. 0.8 - Prob. 5E Ch. 0.8 - Prob. 6E Ch. 0.8 - Prob. 7E Ch. 0.8 - Prob. 8E Ch. 0.8 - Prob. 9E Ch. 0.8 - Prob. 10E Ch. 0.8 - Prob. 11E Ch. 0.8 - Prob. 12E Ch. 0.8 - Prob. 13E Ch. 0.8 - Prob. 14E Ch. 0.8 - Prob. 15E Ch. 0.8 - Prob. 16E Ch. 0.8 - Prob. 17E Ch. 0.8 - Prob. 18E Ch. 0.8 - Prob. 19E Ch. 0.8 - Prob. 20E Ch. 0.8 - Prob. 21E Ch. 0.8 - Prob. 22E Ch. 0.8 - Prob. 23E Ch. 0.8 - Prob. 24E Ch. 0.8 - Prob. 25E Ch. 0.8 - Prob. 26E Ch. 0.8 - Prob. 27E Ch. 0.8 - Prob. 28E Ch. 0.8 - Prob. 29E Ch. 0.8 - Prob. 30E Ch. 0.8 - Prob. 31E Ch. 0.8 - Prob. 32E Ch. 0.8 - Prob. 33E Ch. 0.8 - Prob. 34E Ch. 0.8 - Prob. 35E Ch. 0.8 - Prob. 36E Ch. 0.8 - Prob. 37E Ch. 0.8 - Prob. 38E Ch. 0.8 - Prob. 39E Ch. 0.8 - Prob. 40E Ch. 0.8 - Prob. 41E Ch. 0.8 - Prob. 42E Ch. 0.8 - Prob. 43E Ch. 0.8 - Prob. 44E Ch. 0.8 - Prob. 45E Ch. 0.8 - Prob. 46E Ch. 0.8 - Prob. 47E Ch. 0.8 - Prob. 48E Ch. 0.8 - Prob. 49E Ch. 0.8 - Prob. 50E Ch. 0.8 - Prob. 51E Ch. 0.8 - Prob. 52E Ch. 0.8 - Prob. 53E Ch. 0.8 - Prob. 54E Ch. 0.8 - Prob. 55E Ch. 0.8 - Prob. 56E

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The all real solutions in the polynomial equation x 3 − 1 = 0 .

Solution Summary: The author explains how the polynomial equation x3-1=0 has a real solution, which is x=1.

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Chapter 0 Solutions