Explanation Given Information: The provided polynomial equation is 2 x 6 − x 4 − 2 x 2 + 1 = 0 . Formula used: Principle of 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 Calculation: Consider the polynomial equation 2 x 6 − x 4 − 2 x 2 + 1 = 0 . Make groups in the above polynomial equation then simplify, ( 2 x 6 − x 4 ) + ( − 2 x 2 + 1 ) = 0 x 4 ( 2 x 2 − 1 ) − 1 ( 2 x 2 − 1 ) = 0 ( 2 x 2 − 1 ) ( x 4 − 1 ) = 0 Apply the zero-product rule, If 2 x 2 − 1 = 0 then Add 1 on both sides in the above equation, 2 x 2 − 1 + 1 = 0 + 1 2 x 2 + 0 = 1 2 x 2 = 1 Divide by 2 on both sides, 2 x 2 = 1 2 x 2

7th Edition

ISBN: 9781337291248

Author: Waner, Stefan.

Publisher: Cengage Learning,

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Chapter 0.5, Problem 41E

To determine

To calculate: The all real solutions in the polynomial equation 2x6−x4−2x2+1=0.

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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. (23)2 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 - Prob. 33E 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 - Evaluate expressions in Exercises 3756, rounding...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 - 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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 - Expand each expression in Exercises 122. x(4x+6)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 - Prob. 12E 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 - In Exercises 3148, (a) factor the given...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 - Rewrite each expression in Exercises 116 as a...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 - Prob. 7E Ch. 0.4 - Prob. 8E Ch. 0.4 - Prob. 9E Ch. 0.4 - Prob. 10E Ch. 0.4 - Prob. 11E Ch. 0.4 - Rewrite each expression in Exercises 116 as a...Ch. 0.4 - Prob. 13E Ch. 0.4 - Prob. 14E 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 - By any method, determine all possible real...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 - Prob. 34E 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 - Solve the equations in Exercises 126. x43x3=0 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 - Solve the equations in Exercises 126. 2x3x2x3x+1=0 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 - Sketch the graphs of the equations in Exercises...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 - Find the value of k such that (1,k) is equidistant...Ch. 0.7 - Find the value of k such that (k,k) is equidistant...Ch. 0.7 - Prob. 19E Ch. 0.7 - Describe the set of points (x,y) such that...Ch. 0.8 - Prob. 1E 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 - In Exercises 1728, use the logarithm identities to...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 - Let a=log2,b=log3, and c=log7. 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 2 x 6 − x 4 − 2 x 2 + 1 = 0 .

Solution Summary: The author explains how to calculate the polynomial equation, which has four real solutions: x=pm 1 and sqrt2.

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To calculate: The all real solutions in the polynomial equation 2x6−x4−2x2+1=0.

Chapter 0 Solutions