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 :

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

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

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

These are the intervals

Step 4. Evaluating the value of function at different intervals

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

Step 5. Conclusion

The required interval set is :

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

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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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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

Discrete Mathematics

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Study anywhere. Anytime. Across all devices.

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