   Chapter 0.5, Problem 30E

Chapter
Section
Textbook Problem

By any method, determine all possible real solutions of each equation in Exercises 13–30. Check your answers by substitution. x 3 + 2 x 2 + x = 0

To determine

To calculate: The all real solutions in the polynomial equation x3+2x2+x=0.

Explanation

Given Information:

The provided polynomial equation is x3+2x2+x=0.

Formula used:

Zero product rule:

An equation ab=0

is true if and only if a=0

or b=0,

The value of x

in the equation ax2+bx+c=0

can be given by the quadratic formula,

x=b±b24ac2a

where a,b

and c

are real numbers with a0.

Calculation:

Consider the polynomial equation x3+2x2+x=0.

First determine the single solution in this cubic equation x3+2x2+x=0

Compare the equation x3+2x2+x=0

with the standard cubic equation ax3+bx2+cx+d=0

a=1

and d=0

Therefore, possible factor of 1

is x=±1

and 0

is x=0

First try x=0

substitute in the provided polynomial x3+2x2+x=0,

(0)3+2(0)2+0=?0             0+0+0=?0                     0=0

This is true.

Therefore, x+0

is a factor of the polynomial x3+2x2+x=0.

In order to find other two values of x, divide x3+2x2+x=0

by x+0,

x+0x2+2x+1x3+2x2+x         x3+0x2_                2x2+x               2x2+0x_                        x+0

Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

Let f be the function defined by f(x) = 5x + 6. Find f(3), f(3), f(a), f(a), and f(a + 3).

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

In Problems 1-4, find the intercepts and graph the functions.

Mathematical Applications for the Management, Life, and Social Sciences

Find the derivative of the function. y=cosxsinxln(1+2v)dv

Single Variable Calculus: Early Transcendentals

Proof Prove that for any real number y there exists x in (/2,/2) such that tanx=y.

Calculus: Early Transcendental Functions (MindTap Course List)

π does not exist

Study Guide for Stewart's Multivariable Calculus, 8th

For what values of p does the series converge?

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th 