   Chapter 0.5, Problem 42E

Chapter
Section
Textbook Problem

Find all possible real solutions of each equation in Exercises 31–44. 3 x 6 − x 4 − 12 x 2 + 4 = 0

To determine

To calculate: The all real solutions in the polynomial equation 3x6x412x2+4=0.

Explanation

Given Information:

The provided polynomial equation is 3x6x412x2+4=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 3x6x412x2+4=0.

Make groups in the above polynomial equation then simplify,

(3x612x2)+(x4+4)=03x2(x44)1(x44)=0(x44)(3x21)=0

Apply the zero-product rule,

If 3x21=0 then

Add 1 on both sides in the above equation,

3x21+1=0+13x2+0=13x2=1

Divide by 3 on both sides,

3x2=13x23

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