   Chapter 0.5, Problem 28E

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 − 2 x 2 + 1 = 0

To determine

To calculate: The all real solutions in the polynomial equation x42x2+1=0.

Explanation

Given Information:

The provided polynomial equation is x42x2+1=0.

Formula used:

Principle of zero product rule:

An equation AB=0

is true if and only if A=0

or B=0.

Calculation:

Consider the polynomial equation x42x2+1=0.

Factor the above equation,

x42x2+1=0x4x2x2+1=0x2(x21)1(x21)=0(x21)(x21)=0

Either (x21)=0

or (x21)=0,

If x21=0

then,

on both sides in the above equation,

x21+1=0+1x2+0=1x2=1

Take square root from both sides,

x=±1

If (x21

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