Explanation Given Information: The provided polynomial equation is 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 . Calculation: Consider the polynomial equation x 4 − 2 x 2 + 1 = 0 . Factor the above equation, x 4 − 2 x 2 + 1 = 0 x 4 − x 2 − x 2 + 1 = 0 x 2 ( x 2 − 1 ) − 1 ( x 2 − 1 ) = 0 ( x 2 − 1 ) ( x 2 − 1 ) = 0 Either ( x 2 − 1 ) = 0 or ( x 2 − 1 ) = 0 , If x 2 − 1 = 0 then, Add 1 on both sides in the above equation, x 2 − 1 + 1 = 0 + 1 x 2 + 0 = 1 x 2 = 1 Take square root from both sides, x = ± 1 If ( x 2 − 1

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Author: Stefan Waner, Steven Costenoble

Publisher: Cengage Learning

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Chapter 0.5, Problem 28E

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

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Chapter 0.5, Problem 27E

Chapter 0.5, Problem 29E

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The all real solutions in the polynomial equation x 4 − 2 x 2 + 1 = 0 .

Solution Summary: The author calculates the polynomial equation x42+1=0 based on the principle of zero product rule.

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