Explanation Given Information: The provided polynomial equation is x 4 − 10 x 2 + 9 = 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 x 4 − 10 x 2 + 9 = 0 . Factor the above equation, x 4 − 10 x 2 + 9 = 0 x 4 − ( 9 + 1 ) x 2 + 9 = 0 x 4 − 9 x 2 − x 2 + 9 = 0 x 2 ( x 2 − 9 ) − 1 ( x 2 − 9 ) = 0 ( x 2 − 9 ) ( x 2 − 1 ) = 0 If ( x 2 − 9 ) = 0 then, Add 9 on both sides in the above equation, x 2 − 9 + 9 = 0 + 9 x 2 + 0 = 9 x 2 = 9 Take square root from both sides, x 2 = 9 x = ± 3 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 2 = 1 x = ± 1 Check: For x = 1 Substitute the value of x = 1 in x 4 − 10 x 2 + 9 = 0 . x 4 − 10 x 2 + 9 = 0 ( 1 ) 4 − 10 ( 1 ) 2 + 9 = ? 0 1 − 10 + 9 = ? 0 0 = 0 Which is true

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ISBN: 9780357667286

Author: Waner

Publisher: CENGAGE L

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Chapter 0.5, Problem 27E

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To calculate: The all real solutions in the polynomial equation x4−10x2+9=0.

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Chapter 0.5, Problem 26E

Chapter 0.5, Problem 28E

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The all real solutions in the polynomial equation x 4 − 10 x 2 + 9 = 0 .

Solution Summary: The author calculates the real solutions in the polynomial equation x4-(9+1).

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To calculate: The all real solutions in the polynomial equation x4−10x2+9=0.

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