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 _ �

7th Edition

ISBN: 9781337291248

Author: Waner, Stefan.

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 115–120, factor the expressions over the set of complex numbers. For assistance, consider these examples. • In Section R.3 we saw that some expressions factor over the set of integers. For example: x - 4 = (x + 2)(x – 2). • Some expressions factor over the set of irrational numbers. For example: - 5 = (x + V5)(x – V5). To factor an expression such as x + 4, we need to factor over the set of complex numbers. For example, verify that x + 4 = (x + 2i)(x – 2i). 115. а. х - 9 116. а. х? - 100 117. а. х - 64 b. x + 9 b. + 100 b. x + 64 118. а. х — 25 119. а. х— 3 120. а. х — 11 b. x + 25 b. x + 3 b. x + 11

Exercise 6.3.3 Find the four fourth roots of 16.

For Exercises 19–26, simplify each expression and write the result in standard form, a + bi. 8 + 3i 19. 4 + 5i 20. -4 - 6i 21. 9 - 15i 22. 14 6. -2 -3 -18 + V-48 23. - 20 + V-50 14 - V-98 25. - 10 + V-125 24. 26. 4 10 -7

Chapter 0 Solutions

Applied Calculus

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 - Calculate each expression in Exercises 124, giving...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 - Prob. 38E 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 - Prob. 2E Ch. 0.2 - Evaluate the expression sin Exercises 116. 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In Exercises 2946,...Ch. 0.8 - Prob. 32E Ch. 0.8 - Let a=log2,b=log3, and c=log7. In Exercises 2946,...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