   Chapter 0.3, Problem 47E

Chapter
Section
Textbook Problem

In Exercises 31–48, (a) factor the given expression, and (b) set the expression equal to zero and solve for the unknown (x in the odd-numbered exercises and y in the even-numbered exercises.) x 4 − 5 x 2 + 4

(a)

To determine

To calculate: The factors of the expression x45x2+4.

Explanation

Given information:

The expression, x45x2+4.

Formula used:

Steps to calculate the factors of quadratic equation ax2+bx+c by trial and error method,

Step1: Factor ax2 as (a1x)(a2x) with a1 positive.

Step2: Factor c as c1c2.

Step 3: Check if ax2+bx+c=(a1x±c1)(a2x±c2)

If yes, then (a1x±c1)(a2x±c2) are the factors.

Step 4: If not, try other factorization of ax2 and c and repeat all the steps.

The distributive law,

(a±b)c=ac±bc

Where, a, b and c are any real numbers.

Difference of two squares,

a2b2=(a+b)(ab)

Where, a and b are the real numbers.

Calculation:

Consider the expression,

x45x2+4

Rewrite the above expression as,

(x2)25x2+4

Substitute x2=y in the above expression,

(y)25y+4

Factor of y2 are (y)(y).

The factors of 4 are (1)(4),(4)(1),(2)(2),(1)(4)and (4)(1).

Consider the factors (y)(y) and (1)(4)

(b)

To determine

To calculate: The value of x when the expression x45x2+4 is equal to zero.

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