Chapter 4: Q. 22 (page 241)

Solve the inequality algebraically
$x^{3} + 8 x^{2} < 0$

Short Answer

Expert verified

Required solution set is $(- \infty, - 8)$ .

Step by step solution

Step 1. Given information

We are given an inequality,

$x^{3} + 8 x^{2} < 0$

Step 2.Finding the zeros

The zeros are given by,

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

So, the intervals will be,

$(- \infty, - 8), (- 8, 0) and (0, \infty)$

Step 4. Selecting a test number in each interval

The table is as follows,

Interval	$(- \infty, - 8)$	$(- 8, 0)$	$(0, \infty)$
Chosen Number	$- 10$	$- 1$	$1$
Value of Function	localid="1646303382470" $f (- 10) = - 200$	$f (- 1) = 7$	$f (1) = 9$
Check	Negative	Positive	Positive

Hence the solution set is $(- \infty, - 8)$ .

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Solve the inequality algebraically
$x^{3} + 8 x^{2} < 0$

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 algebraicallyx3+8x2<0

Short Answer

Step by step solution

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Solve the inequality algebraically
$x^{3} + 8 x^{2} < 0$