Q. 28 x3+2x2-3x聽>0... [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)

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

Short Answer

Expert verified

The required interval is $(- 3, 0) 鈭� (1, 鈭�)$

Step by step solution

Step 1. Given Information

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

This is given to us . we need to solve for x .

Step 2. Factorization

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

The zeros of the equation are 0, 1 & -3

Step 3. Dividing the number line into intervals using the above zeros.

The intervals are :

$(- 鈭�, - 3) (- 3, 0) (0, 1) (1, 鈭�)$

Step 4. Evaluating the value of function

$1 . (- 鈭�, - 3) l e t n u m b e r b e - 4 v a l u e o f f u n c t i o n a t - 4 = - 20 c o n d i t i o n n o t s a t i s f i e d . 2 . (- 3, 0) L e t n u m b e r b e - 1 v a l u e o f f u n c t i o n a t - 1 = 4 T h e c o n d i t i o n i s s a t i s f i e d . 3 . (0, 1) l e t n u m b e r b e 0.1 v a l u e o f f u n c t i o n a t 0.1 = - 0.099 c o n d i t i o n n o t s a t i s f i e d . 4 . (0, 鈭�) L e t n u m b e r b e 2 v a l u e o f f u n c t i o n a t 2 = 10 T h e c o n d i t i o n i s s a t i s f i e d .$

Step 5. conclusion

The required interval is $(- 3, 0) 鈭� (1, 鈭�)$

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91影视

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

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Factorization

Step 3. Dividing the number line into intervals using the above zeros.

Step 4. Evaluating the value of function

Step 5. conclusion

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91影视

x3+2x2-3x>0

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Factorization

Step 3. Dividing the number line into intervals using the above zeros.

Step 4. Evaluating the value of function

Step 5. conclusion

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Applied Mathematics

Statistics

Geometry

Pure Maths

Mechanics Maths

Study anywhere. Anytime. Across all devices.

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