Chapter 4: Q. 94 (page 210)

One solution of the equation $x^{3} + 5 x^{2} + 5 x - 2 = 0$ is $- 2$ .
Find the sum of the remaining solutions.

Short Answer

Expert verified

If $- 2$ is a solution of the equation $x^{3} + 5 x^{2} + 5 x - 2 = 0$ then the sum of the remaining solutions will be $- 3$

Step by step solution

Step 1. given data

The given equation is

$x^{3} + 5 x^{2} + 5 x - 2 = 0$

one solution of the equation is $- 2$

Step 2. factorize the equation

one solution of the equation is $x = - 2$

so $x + 2 = 0$

divide the expression $x^{3} + 5 x^{2} + 5 x - 2$ by $x + 2$

$\frac{x + 2 \begin{matrix} x^{2} + 3 x - 1 \end{matrix} \begin{matrix} x^{3} + 5 x^{2} + 5 x - 2 \\ - (x^{3} + 2 x^{2}) \end{matrix}}{\frac{\begin{matrix} 3 x^{2} + 5 x - 2 \\ - (3 x^{2} + 6 x) \end{matrix}}{\frac{\begin{matrix} - x - 2 \\ - (x - 2) \end{matrix}}{0}}}$

so the equation can be factorized as $(x + 2) (x^{2} + 3 x - 1) = 0$

Step 3. Apply the quadratic formula

use the quadratic formula to find the solution of $(x^{2} + 3 x - 1)$

$x = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a} x = \frac{- 3 \pm \sqrt{3^{2} - 4 (1) (- 1)}}{2 (1)} x = \frac{- 3 \pm \sqrt{13}}{2} x = \frac{- 3 + \sqrt{13}}{2}, \frac{- 3 - \sqrt{13}}{2}$

Step 4. the sum of solutions

Sum of solutions of the equation except $x = - 2$

$\frac{- 3 + \sqrt{13}}{2} + \frac{- 3 - \sqrt{13}}{2} = \frac{- 3 + \sqrt{13} - 3 - \sqrt{13}}{2} = \frac{- 6}{2} = - 3$

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

One solution of the equation $x^{3} + 5 x^{2} + 5 x - 2 = 0$ is $- 2$ .
Find the sum of the remaining solutions.

Short Answer

Step by step solution

Step 1. given data

Step 2. factorize the equation

Step 3. Apply the quadratic formula

Step 4. the sum of solutions

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Decision Maths

Logic and Functions

Statistics

Calculus

Pure Maths

Study anywhere. Anytime. Across all devices.

One solution of the equation x3+5x2+5x-2=0 is -2.Find the sum of the remaining solutions.

Short Answer

Step by step solution

Step 1. given data

Step 2. factorize the equation

Step 3. Apply the quadratic formula

Step 4. the sum of solutions

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Decision Maths

Logic and Functions

Statistics

Calculus

Pure Maths

Study anywhere. Anytime. Across all devices.

One solution of the equation $x^{3} + 5 x^{2} + 5 x - 2 = 0$ is $- 2$ .
Find the sum of the remaining solutions.