Q. 28 Solve the inequality algebraical... [FREE SOLUTION]

91影视

Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 4: Q. 28 (page 242)

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

Short Answer

Expert verified

The required interval set is :

$(- 3, 0) 鈭� (1, 鈭�)$

Step by step solution

Step 1. Given inequality

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

we need to solve for x.

Step 2. Factorization

$x^{3} + 2 x^{2} - 3 x > 0 x (x^{2} + 2 x - 3) > 0 x (x^{2} + 3 x - x - 3) > 0 x (x (x + 3) - 1 (x + 3)) > 0 x (x - 1) (x + 3) > 0$

The zeros of the above equation are : 0,1,-3

Step 3. Dividing the number line into 4 intervals

$(- 鈭�, - 3) (- 3, 0) (0, 1) (1, 鈭�)$

These are the intervals

Step 4. Evaluating the value of function at different intervals

$1 . (- 鈭�, - 3) L e t u s t a k e n u m b e r - 4 T h e v a l u e o f t h e f u n c t i o n a t - 4 = - 20 t h e c o n d i t i o n i s n o t s a t i s f i e d . 2 . (- 3, 0) L e t u s t a k e n u m b e r - 1 T h e v a l u e o f t h e f u n c t i o n a t - 1 = 4 t h e c o n d i t i o n i s s a t i s f i e d . 3 . (0, 1) L e t u s t a k e n u m b e r 0.1 T h e v a l u e o f t h e f u n c t i o n a t 0.1 = - 0.279 t h e c o n d i t i o n i s n o t s a t i s f i e d . 4 . (1, 鈭�) L e t u s t a k e n u m b e r 2 T h e v a l u e o f t h e f u n c t i o n a t 2 = 10 t h e c o n d i t i o n i s s a t i s f i e d .$

Step 5. Conclusion

The required interval set is :

$(- 3, 0) 鈭� (1, 鈭�)$

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91影视

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

Short Answer

Step by step solution

Step 1. Given inequality

Step 2. Factorization

Step 3. Dividing the number line into 4 intervals

Step 4. Evaluating the value of function at different intervals

Step 5. Conclusion

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91影视

Solve the inequality algebraically.x3+2x2-3x>0

Short Answer

Step by step solution

Step 1. Given inequality

Step 2. Factorization

Step 3. Dividing the number line into 4 intervals

Step 4. Evaluating the value of function at different intervals

Step 5. Conclusion

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Discrete Mathematics

Probability and Statistics

Decision Maths

Pure Maths

Calculus

Study anywhere. Anytime. Across all devices.

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