Chapter 4: Q. 21 (page 241)

Solve the inequality algebraically
$x^{3} - 4 x^{2} > 0$

Short Answer

Expert verified

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

Step by step solution

Step 1. Given information

We are given an inequality,

$x^{3} - 4 x^{2} > 0$

Step 2.Finding the zeros

The zeros are given by,

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

So, the intervals will be,

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

Step 4. Selecting a test number in each interval

The table is as follows,

Interval	$(- \infty, 0)$	$(0, 4)$	$(4, \infty)$
Chosen Number	$- 1$	$1$	$5$
Value of Function	$f (- 1) = - 5$	$f (1) = - 3$	$f (5) = 25$
Check	Negative	Negative	Positive

Hence the solution set is $(4, \infty)$ .

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Solve the inequality algebraically
$x^{3} - 4 x^{2} > 0$

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 algebraicallyx3-4x2>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

One App. One Place for Learning.

Most popular questions from this chapter

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Solve the inequality algebraically
$x^{3} - 4 x^{2} > 0$