   Chapter 0.5, Problem 40E

Chapter
Section
Textbook Problem

Find all possible real solutions of each equation in Exercises 31–44. x 3 − x 2 − 3 x + 3 = 0

To determine

To calculate: The all real solutions in the polynomial equation x3x23x+3=0.

Explanation

Given Information:

The provided polynomial equation is x3x23x+3=0.

Formula used:

Zero product rule:

An equation ab=0 is true if and only if a=0 or b=0, both

A product is zero if and only if at least one factor is zero

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 x3x23x+3=0.

First determine the single solution in this cubic equation x3x23x+3=0

Compare the equation x3x23x+3=0 with the standard cubic equation ax3+bx2+cx+d=0.

a=1 and d=3

Therefore, possible factor of 1 is x=±1 and 3 is x=±1, x=±3.

First try x=1 substitute in the provided polynomial equation x3x23x+3=0, (1)3(1)23(1)+3=?0             113+3=?0                           0=0

Which is true

Therefore, x1 is a factor of the polynomial x3x23x+3=0.

In order to find other two values of x, divide x3x23x+3=0 by x1, x1x23x3x23x+3         x3x2_                   3x+3                   3x+3_                           0

Thus,

x3x23x+3=(x1)(x23)

Therefore,

(x1)(x23)=0

Apply the principle of zero-product,

Either x1=0 or x23=0

If x1=0 then,

Add 1 on both sides,

x1+1=0+1x+0=1x=1

If (x23)=0

Compare the above equation with the equation ax2+bx+c=0, a=1, b=0 and c=3

Put the values of a,b,c in the quadratic formula x=b±b24ac2a

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

Expand each expression in Exercises 122. (2y+3)(y+5)

Finite Mathematics and Applied Calculus (MindTap Course List)

Evaluate the integral, if it exists. csc2x1+cotxdx

Single Variable Calculus: Early Transcendentals, Volume I

In Exercises 7-28, perform the indicated operations and simplify each expression. 22. 2x(x+1)1/2(x+1)1/2x2

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

In Problems 25-38, find y'. 30.

Mathematical Applications for the Management, Life, and Social Sciences

Factor completely. 36x2

Trigonometry (MindTap Course List) 