Book edition 6th

Author(s) Sullivan

Pages 1200 pages

ISBN 9780321795465

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Short Answer

Solve the inequality algebraically
$x^{3} - 2 x^{2} - 3 x > 0$

Required solution set is $(- 1, 0) \cup (3, \infty)$

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Given information

we have a given inequality

$x^{3} - 2 x^{2} - 3 x > 0$

Step 2.Finding the zeros

Zeros of inequality

$f (x) = x^{3} - 2 x^{2} - 3 x > 0 a r e f (x) = 0 x^{3} - 2 x^{2} - 3 x = 0 x (x^{2} - 2 x - 3) = 0 x (x - 3) (x + 1) = 0 x = 0 x = 3 x = - 1$

Step 3.Divide the real number line into 4 intervals

Now we use the zeros to separate the real number line into intervals.

$(- \infty, - 1) (- 1, 0) (0, 3) (3, \infty)$

Step 4.Selecting a test number in each interval

Now we select a test number in each interval found in Step 3 and evaluate at each number to determine if $f (x) = x^{3} - 2 x^{2} - 3 x = 0$ is positive or negative.

In the interval $(- \infty, - 1)$ we chose -2 where f is negative

In the interval $(- 1, 0)$ we chose -0.5 , where f is positive.

In the interval (0,3) we chose 2.5 , where f is negative.

In the interval $(3, \infty)$ we chose 4 , where f is positive.

We know that our required inequality is $f (x) > 0$

Here the inequality is not strict $(\geq o r \leq)$ so we have to exclude the solutions of $f (x) = 0$ in the solution set.

So we want the interval where f is positive.

So the required solution set is $(- 1, 0) \cup (3, \infty)$

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Precalculus Enhanced with Graphing Utilities

Answers without the blur.

Short Answer

Solve the inequality algebraically
$x^{3} - 2 x^{2} - 3 x > 0$

Step by Step Solution

Step 1. Given information

Step 2.Finding the zeros

Step 3.Divide the real number line into 4 intervals

Step 4.Selecting a test number in each interval

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Step 2.Finding the zeros

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Solve the inequality algebraically
$x^{3} - 2 x^{2} - 3 x > 0$