Chapter 4: Q. 23 (page 241)

Solve the inequality algebraically
$2 x^{3} > - 8 x^{2}$

Short Answer

Expert verified

Required solution set is $(- 4, 0) \cup (0, \infty)$ .

Step by step solution

Step 1. Given information

We are given an inequality,

$2 x^{3} > - 8 x^{2}$

Step 2.Finding the zeros

The zeros is given by,

$2 x^{3} = - 8 x^{2} 2 x^{3} + 8 x^{2} = 0 2 x^{2} (x + 4) = 0 2 x^{2} = 0 x = 0 x + 4 = 0 x = - 4$

So, the intervals will be,

$(- \infty, - 4), (- 4, 0), and (0, \infty)$

Step 4. Selecting a test number in each interval

The table is as follows,

Interval	$(- \infty, - 4)$	$(- 4, 0)$	$(0, \infty)$
Chosen Number	$- 5$	$- 1$	$1$
Value of Function	$f (- 5) = - 50$	$f (- 1) = 6$	$f (1) = 10$
Check	Negative	Positive	Positive

Hence the solution set is localid="1646304433911" $(- 4, 0) \cup (0, \infty)$ .

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Solve the inequality algebraically
$2 x^{3} > - 8 x^{2}$

Short Answer

Step by step solution

Step 1. Given information

Step 2.Finding the zeros

Step 4. Selecting a test number in each interval

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Solve the inequality algebraically2x3>-8x2

Short Answer

Step by step solution

Step 1. Given information

Step 2.Finding the zeros

Step 4. Selecting a test number in each interval

One App. One Place for Learning.

Most popular questions from this chapter

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Solve the inequality algebraically
$2 x^{3} > - 8 x^{2}$