Chapter 1: Q. 31 (page 29)

In Problem 17-36, solve each equation algebraically. Verify your solution using a graphing utility.
$x^{3} + x^{2} - 4 x - 4 = 0$

Short Answer

Expert verified

The required solutions are $x_{1} = - 1, x_{2} = - 2, x_{3} = 2$ and the graph of the solution is given below:

Step by step solution

Step 1. Given information.

We have:

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

Step 2. Solve the equation algebraically.

The equation is $x^{3} + x^{2} - 4 x - 4 = 0$ .

Take the common out from the groups:

$x^{2} (x - 1) - 4 (x - 1) = 0 (x^{2} - 4) (x - 1) = 0 (x^{2} - 2^{2}) (x - 1) = 0$

Apply the difference of two squares formula: $x^{2} - y^{2} = (x + y) (x - y)$

role="math" localid="1645785489502" $(x + 2) (x - 2) (x - 1) = 0 x = - 2, 1, 2$

Step 3. Verify the solution using a graphing utility.

The solution of the equation are $x = - 1, x = - 2, x = 2$ .
Draw the graph of the equation $x^{3} + x^{2} - 4 x - 4 = 0$ using the graphing utility:

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In Problem 17-36, solve each equation algebraically. Verify your solution using a graphing utility.
$x^{3} + x^{2} - 4 x - 4 = 0$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Solve the equation algebraically.

Step 3. Verify the solution using a graphing utility.

One App. One Place for Learning.

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In Problem 17-36, solve each equation algebraically. Verify your solution using a graphing utility.x3+x2-4x-4=0

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Solve the equation algebraically.

Step 3. Verify the solution using a graphing utility.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Geometry

Pure Maths

Probability and Statistics

Statistics

Calculus

Study anywhere. Anytime. Across all devices.

In Problem 17-36, solve each equation algebraically. Verify your solution using a graphing utility.
$x^{3} + x^{2} - 4 x - 4 = 0$