Explanation Procedure used: 1 . Find an equivalent inequality with P ( x ) on one side and 0 on the other. 2. Change the inequality symbol to an equals sign and solve the related equation; that is, solve P ( x ) = 0 . 3. Use the solutions to divide the x axis into intervals. Then select a test value from each interval and determine the sign of the polynomial on the interval. 4. determine the intervals for which the inequality is satisfied and write intervals notation or set builder notation for the solution set. Include the endpoints of the intervals in the solution set if the inequality symbol is ≤ or ≥ . Calculation: The given polynomial inequality is x 4 − 27 x 2 − 14 x + 120 ≥ 0 . By the procedure from 1 to 4, find the solution set of the inequality. Change the inequlity sign by equal sign to form related equation as x 4 − 27 x 2 − 14 x + 120 = 0 . From the graph, the x intercept of the related function occurs at x = − 4 , x = − 3 , x = 2 and x = 5 . Thus, the solution set is { − 4 , − 3 , 2 , 5 }

College Algebra: Graphs and Models (6th Edition)

6th Edition

ISBN: 9780134179032

Author: Marvin L. Bittinger, Judith A. Beecher, David J. Ellenbogen, Judith A. Penna

Publisher: PEARSON

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Chapter 4.6, Problem 22E

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To solve: The polynomial inequality x4−27x2−14x+120≥0.

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Chapter 4.6, Problem 21E

Chapter 4.6, Problem 23E

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Chapter 4 Solutions

College Algebra: Graphs and Models (6th Edition)

Ch. 4.1 - Determine the leading term, the leading...Ch. 4.1 - Prob. 2E Ch. 4.1 - Determine the leading term, the leading...Ch. 4.1 - Prob. 4E Ch. 4.1 - Prob. 5E Ch. 4.1 - Determine the leading term, the leading...Ch. 4.1 - Prob. 7E Ch. 4.1 - Prob. 8E Ch. 4.1 - Determine the leading term, the leading...Ch. 4.1 - Prob. 10E

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The polynomial inequality x 4 − 27 x 2 − 14 x + 120 ≥ 0 .

Solution Summary: The author explains how to solve the polynomial inequality by changing the inequality symbol to an equals sign and solving the related equation.

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To solve: The polynomial inequality x4−27x2−14x+120≥0.

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Chapter 4 Solutions