Explanation Definition used: General quadratic equation : “Given that a , b , and c are constant ( a ≠ 0 ) , the equation a x 2 + b x 2 + c = 0 is called the general quadratic equation in x ”. Calculation: Consider the equation x 4 − 17 x 2 + 16 = 0 . In order to find the value of x , first rewrite the equation in quadratic form. Substitute y = x 2 in x 4 − 17 x 2 + 16 = 0 and simplify the equation as follows. y 2 − 17 y + 16 = 0 y 2 − 16 y − y + 16 = 0 y ( y − 16 ) − 1 ( y − 16 ) = 0 ( y − 16 ) ( y − 1 ) = 0 On further simplification, y − 16 = 0 or y − 1 = 0 y = 16 or y = 1 x 2 = 16 or x 2 = 1 [ ∵ y = x 2 ] x = ± 4 or x = ± 1 Thus, the solutions of the equation is x = ± 4 and x = ± 1 _ . Check the solution by substituting x = 4 in x 4 − 17 x 2 + 16 = 0 . ( 4 ) 4 − 17 ( 4 ) 2 + 16 = ? 0 256 − 17 ( 16 ) + 16 = ? 0 256 − 272 + 16 = ? 0 0 = ? 0 [ True ] Check the solution by substituting x = − 4 in x 4 − 17 x 2 + 16 = 0

Basic Technical Mathematics with Calculus (11th Edition)

11th Edition

ISBN: 9780134437736

Author: Allyn J. Washington, Richard Evans

Publisher: PEARSON

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Chapter 14 Solutions

Basic Technical Mathematics with Calculus (11th Edition)

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 x 4 − 17 x 2 + 16 = 0 .

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