Explanation Formula used: Quadratic formula : For a quadratic equation of the form a x 3 + b x + c = 0 the solutions are x = − b ± b 2 − 4 a c 2 a . Procedure used: Solving radical equations: 1. Isolate a single radical on one side of the equation. 2. Square both sides of the equation. (Or raise both sides to a power that is equal to the index of the radical.). 3. If a radica1 remains, repeat steps 1 and 2. 4. Solve the resulting equation. 5. All solutions must be checked in the original equation, and only those that satisfy the original equation are actual solutions. Calculation: By using above procedure, the given equation can be solved as follows. The given equation can be written as follows. ( x 2 ) 2 − 5 ( x 2 ) + 4 = 0 Let u = x 2 . Then the above equation becomes u 2 − 5 u + 4 = 0 . Use the above formula to simplify the equation u 2 − 5 u + 4 = 0 . Substitute a = 1 , b = − 5 and c = 4 in the quadratic formula to find the value of u . u = 5 ± ( − 5 ) 2 − 4 ( 1 ) ( 4 ) 2 ( 1 ) = 5 ± 25 − 16 2 = 5 ± 9 2 = 5 ± 3 2 On further simplification, u = 5 + 3 2 or 5 − 3 2 = 8 2 or 2 2 = 4 or 1 To find the value of x substitute u = 4 in x 2 = u

College Algebra in Context with Applications for the Managerial, Life, and Social Sciences (5th Edition)

5th Edition

ISBN: 9780134179025

Author: Ronald J. Harshbarger, Lisa S. Yocco

Publisher: PEARSON

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A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.

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Chapter 4.4, Problem 15E

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To solve: The equation x4−5x2+4=0 algebraically and check the solution graphically or by substitution.

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Chapter 4.4, Problem 14E

Chapter 4.4, Problem 16E

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Chapter 4 Solutions

College Algebra in Context with Applications for the Managerial, Life, and Social Sciences (5th Edition)

Ch. 4.1 - In Exercises 116, (a) sketch the graph of each...Ch. 4.1 - In Exercises 116, (a) sketch the graph of each...Ch. 4.1 - Prob. 3E Ch. 4.1 - Prob. 4E Ch. 4.1 - Prob. 5E Ch. 4.1 - In Exercises 116, (a) sketch the graph of each...Ch. 4.1 - Prob. 7E Ch. 4.1 - Prob. 8E Ch. 4.1 - Prob. 9E Ch. 4.1 - Prob. 10E

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The equation x 4 − 5 x 2 + 4 = 0 algebraically and check the solution graphically or by substitution.

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