Explanation Definition used: General quadratic equation : “Given that a , b , and c are constant ( a ≠ 0 ) , the equation a x 2 + b x + c = 0 is called the general quadratic equation in x ”. Calculation: Consider the equation 1 s 2 + 1 + 2 s 2 + 3 = 1 . Rewrite the equation as follows. 1 s 2 + 1 + 2 s 2 + 3 = 1 ( s 2 + 3 ) + 2 ( s 2 + 1 ) ( s 2 + 1 ) ( s 2 + 3 ) = 1 s 2 + 3 + 2 s 2 + 2 = s 4 + 4 s 2 + 3 s 4 + s 2 − 2 = 0 In order to find the value of s , first rewrite the equation in quadratic form. Substitute s 2 = y in s 4 + s 2 − 2 = 0 and simplify the equation as follows. y 2 + y − 2 = 0 y 2 + 2 y − y − 2 = 0 y ( y + 2 ) − 1 ( y + 2 ) = 0 ( y + 2 ) ( y − 1 ) = 0 On further simplification, y = − 2 or y = 1 s 2 = − 2 or s 2 = 1 [ ∵ y = s 2 ] s = ± j 2 or s = ± 1 Thus, the solutions of the equation are s = ± j 2 and s = ± 1 _

Pearson eText for Basic Technical Mathematics with Calculus -- Instant Access (Pearson+)

11th Edition

ISBN: 9780137554843

Author: Allyn Washington, Richard Evans

Publisher: PEARSON+

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Chapter 14.3, Problem 25E

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Chapter 14.3, Problem 24E

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Chapter 14 Solutions

Pearson eText for Basic Technical Mathematics with Calculus -- Instant Access (Pearson+)

Ch. 14.1 - In Example 7, determine how many times the rocket...Ch. 14.1 - Prob. 1E Ch. 14.1 - Prob. 2E Ch. 14.1 - Prob. 3E Ch. 14.1 - Prob. 4E Ch. 14.1 - Prob. 5E Ch. 14.1 - Prob. 6E Ch. 14.1 - Prob. 7E Ch. 14.1 - Prob. 8E Ch. 14.1 - Prob. 9E

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The equation 1 s 2 + 1 + 2 s 2 + 3 = 1 algebraically.

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Chapter 14 Solutions