Chapter 4: Q. 41 (page 246)

Solve each inequality. Graph the solution set.
$x^{3} + x^{2} < 4 x + 4$

Short Answer

Expert verified

The real zeroes are $- 1, 2, - 2$ and the solution set can be graphed as

Step by step solution

Step 1. Given Information

The given inequality is $x^{3} + x^{2} < 4 x + 4$

Step 2. Calculation

Solve the given inequality as follows,

$x^{3} + x^{2} - 4 x - 4 < 4 x + 4 - 4 x - 4 x^{3} + x^{2} - 4 x - 4 < 0 x^{3} + x^{2} - 4 x - 4 = 0 x^{2} (x + 1) - 4 (x + 1) = 0 (x + 1) (x^{2} - 4) = 0 x + 1 = 0 \Rightarrow x = - 1 x^{2} - 4 = 0 \Rightarrow x = \pm 2$

Thus, the real zeroes of function are $- 1, 2 a n d - 2$

Step 3. Graph

Construct the table by using a number from each interval to check whether the function is positive or negative.

Thus, the solution set is $(- \infty, - 2) \cup (- 1, 2)$

And the solution set can be graphed as

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Solve each inequality. Graph the solution set.
$x^{3} + x^{2} < 4 x + 4$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Calculation

Step 3. Graph

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Solve each inequality. Graph the solution set.x3+x2<4x+4

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Calculation

Step 3. Graph

One App. One Place for Learning.

Most popular questions from this chapter

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Solve each inequality. Graph the solution set.
$x^{3} + x^{2} < 4 x + 4$