   Chapter 0.5, Problem 39E

Chapter
Section
Textbook Problem

Find all possible real solutions of each equation in Exercises 31–44. x 3 − x 2 − 5 x + 5 = 0

To determine

To calculate: The all real solutions in the polynomial equation x3x25x+5=0.

Explanation

Given Information:

The provided polynomial equation is x3x25x+5=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 x3x25x+5=0.

First determine the single solution in this cubic equation x3x25x+5=0

Compare the equation x3x25x+5=0 with the standard cubic equation ax3+bx2+cx+d=0.

a=1 and d=5

Therefore, possible factor of 1 is x=±1 and 5 is x=±1, x=±5.

First try x=1 substitute in the provided polynomial equation x3x25x+5=0, (1)3(1)25(1)+5=?0             115+5=?0                            0=0

Which is true.

Therefore, x1 is a factor of the polynomial x3x25x+5=0.

In order to find other two values of x, divide x3x25x+5=0 by x1, x1x25x3x25x+5         x3x2_                   5x+5                   5x+5_                           0

Thus,

x3x25x+5=(x1)(x25)

Therefore,

(x1)(x25)=0

Apply the principle of zero-product,

Either x1=0 or x25=0

If x1=0 then,

Add 1 on both sides,

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

If (x25)=0 then

Compare the above equation with the equation ax2+bx+c=0, a=1, b=0 and c=5

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

Evaluate limn1n[(1n)9+(2n)9+(3n)9++(nn)9]

Single Variable Calculus: Early Transcendentals, Volume I

In Exercises 2934, rationalize the denominator of each expression. 34. 2a+b2ab

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

How fast is the angle between the hands of an analog clock increasing at 3:30 pm? 2π radians/hr

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

True or False: Let . Then f(x, y) is a joint probability function.

Study Guide for Stewart's Multivariable Calculus, 8th 