Chapter 4: Q. 28 (page 242)

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

Short Answer

Expert verified

The required interval is $(- 3, 0) \cup (1, \infty)$

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 :

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

Step 4. Evaluating the value of function

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

Step 5. conclusion

The required interval is $(- 3, 0) \cup (1, \infty)$

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

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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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

Pure Maths

Theoretical and Mathematical Physics

Statistics

Geometry

Logic and Functions

Decision Maths

Study anywhere. Anytime. Across all devices.

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