   Chapter 0.5, Problem 29E

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 4 + x 2 − 1 = 0

To determine

To calculate: The all real solutions in the polynomial equation x4+x21=0.

Explanation

Given Information:

The provided polynomial equation is x4+x21=0.

Formula used:

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 x4+x21=0.

The above polynomial equation can be written as (x2)2+x21=0

Let x2=t put in the polynomial equation (x2)2+x21=0

t2+t1=0

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

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

t=1±(1)241(1)21=1±1+42=1±52

Further simplify,

Put 1±52 in x2=t, x2=t=1±52

Take square root from both sides,

x=±1±52

Check:

For x=1±52

Substitute x=1±52 in the equation x4+x21=0 then simplify,

(1±52)4+(1±52)21=?0(1±52)2+(1±52)1=?0

Taking positive (+) sign from the above equation then simplify,

(1+52)2+(1+52)1=?01+5254+1+521=?06252+2544=?00=0

Which is true

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

Find the mean for the scores in the following frequency distribution table: X f 6 1 5 4 4 2 3 2 2 1

Essentials of Statistics for The Behavioral Sciences (MindTap Course List)

Find each product. x(3x22x+5)

Elementary Technical Mathematics

Finding a Limit In Exercises 63-74, find the limit, if it exists. limx14xx+1

Calculus: Early Transcendental Functions (MindTap Course List)

45 15 63 127

Study Guide for Stewart's Multivariable Calculus, 8th

True or False: f(a)=lima0f(a+h)f(a)h.

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

Find the effective rate corresponding to 623%/year compounded quarterly.

Finite Mathematics for the Managerial, Life, and Social Sciences 