Explanation Given Information: The given inequality is 3 x 2 − 6 x + 2 ≤ 0 . Formula used: According to the quadratic formula, for a quadratic equation a x 2 + b x + c = 0 , the value of x is found using, x = − b ± b 2 − 4 a c 2 a To solve a quadratic inequality, perform the following steps: Step 1: The inequality is written as an equation. Step 2: Use the solution from Step 1 and determine the intervals, and graph them on a number line. Step 3: To determine the suitable intervals that satisfy the inequality substitute a test value from each interval into the original inequality. Step 4: Separately, consider the endpoints. If the end point is included then the inequality has the symbol ≤ or ≥ . Calculation: Consider the inequality, 3 x 2 − 6 x + 2 ≤ 0 Solve the equation, 3 x 2 − 6 x + 2 = 0 Compare the equation with the standard quadratic equation, a x 2 + b x + c = 0 , ( a ≠ 0 ) . Here, a = 3 , b = − 6 and c = 2 Recall that the quadratic formula is given by, x = − b ± b 2 − 4 a c 2 a Substitute 3 for a , -6 for b and 2 for c . x = − ( − 6 ) ± ( − 6 ) 2 − 4 ( 3 ) ( 2 ) 2 ( 3 ) Simplify the radical. x = − ( − 6 ) ± ( − 6 ) 2 − 4 ( 3 ) ( 2 ) 2 ( 3 ) = 6 ± 36 − 24 2 ( 3 ) = 6 ± 12 2 ( 3 ) Take the square root and a common factor from numerator and denominator. x = 6 ± 2 3 2 ( 3 ) = 2 ( 3 ± 3 ) 2 ( 3 ) = 3 ± 3 3 Therefore, the solution set for the quadratic equation 3 x 2 − 6 x + 2 = 0 is { 3 ± 3 3 } . Now, plot the values 3 + 3 3 and 3 − 3 3 on the number line and divide the number line into three intervals. The first interval is from − ∞ to 3 − 3 3 , second interval is from 3 − 3 3 to 3 + 3 3 and the third interval is from 3 + 3 3 to ∞

Beginning and Intermediate Algebra (6th Edition)

6th Edition

ISBN: 9780321969163

Author: Margaret L. Lial, John Hornsby, Terry McGinnis

Publisher: PEARSON

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Chapter 11.8, Problem 24E

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To calculate: The solution set for the inequality 3x2−6x+2≤0 and graph it.

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Chapter 11.8, Problem 23E

Chapter 11.8, Problem 25E

Chapter 11 Solutions

Beginning and Intermediate Algebra (6th Edition)

Ch. 11.1 - Concept Check Answer each question. 1. Which of...Ch. 11.1 - Prob. 2E Ch. 11.1 - Prob. 3E Ch. 11.1 - Prob. 4E Ch. 11.1 - Solve each equation using the zero-factor...Ch. 11.1 - Prob. 6E Ch. 11.1 - Solve each equation using the zero-factor...Ch. 11.1 - Prob. 8E Ch. 11.1 - Solve each equation using the zero-factor...Ch. 11.1 - Prob. 10E

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The solution set for the inequality 3 x 2 − 6 x + 2 ≤ 0 and graph it.

Solution Summary: The author explains how to solve a quadratic inequality using the following steps: equation, intervals, and endpoints.

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To calculate: The solution set for the inequality 3x2−6x+2≤0 and graph it.

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Chapter 11 Solutions