   Chapter 0.5, Problem 41E

Chapter
Section
Textbook Problem

Find all possible real solutions of each equation in Exercises 31–44. 2 x 6 − x 4 − 2 x 2 + 1 = 0

To determine

To calculate: The all real solutions in the polynomial equation 2x6x42x2+1=0.

Explanation

Given Information:

The provided polynomial equation is 2x6x42x2+1=0.

Formula used:

Principle of 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

Calculation:

Consider the polynomial equation 2x6x42x2+1=0.

Make groups in the above polynomial equation then simplify,

(2x6x4)+(2x2+1)=0x4(2x21)1(2x21)=0(2x21)(x41)=0

Apply the zero-product rule,

If 2x21=0 then

Add 1 on both sides in the above equation,

2x21+1=0+12x2+0=12x2=1

Divide by 2 on both sides,

2x2=12x2

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