(a) Explanation Given information: The expression, x 4 − 5 x 2 + 4 . Formula used: Steps to calculate the factors of quadratic equation a x 2 + b x + c by trial and error method, Step1: Factor a x 2 as ( a 1 x ) ( a 2 x ) with a 1 positive. Step2: Factor c as c 1 c 2 . Step 3: Check if a x 2 + b x + c = ( a 1 x ± c 1 ) ( a 2 x ± c 2 ) If yes, then ( a 1 x ± c 1 ) ( a 2 x ± c 2 ) are the factors. Step 4: If not, try other factorization of a x 2 and c and repeat all the steps. The distributive law, ( a ± b ) c = a c ± b c Where, a, b and c are any real numbers. Difference of two squares, a 2 − b 2 = ( a + b ) ( a − b ) Where, a and b are the real numbers. Calculation: Consider the expression, x 4 − 5 x 2 + 4 Rewrite the above expression as, ( x 2 ) 2 − 5 x 2 + 4 Substitute x 2 = y in the above expression, ( y ) 2 − 5 y + 4 Factor of y 2 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 x 4 − 5 x 2 + 4 is equal to zero.

7th Edition

ISBN: 9781337291248

Author: Waner, Stefan.

Publisher: Cengage Learning,

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Question

Chapter 0.3, Problem 47E

(a)

To determine

To calculate: The factors of the expression x4−5x2+4.

(b)

To determine

To calculate: The value of x when the expression x4−5x2+4 is equal to zero.

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Chapter 0.3, Problem 46E

Chapter 0.3, Problem 48E

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Chapter 0 Solutions

Applied Calculus

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Ch. 0.1 - Prob. 11E Ch. 0.1 - Prob. 12E Ch. 0.1 - Prob. 13E Ch. 0.1 - Calculate each expression in Exercises 124, giving...Ch. 0.1 - Prob. 15E Ch. 0.1 - Prob. 16E Ch. 0.1 - Calculate each expression in Exercises 124, giving...Ch. 0.1 - Prob. 18E Ch. 0.1 - Prob. 19E Ch. 0.1 - Prob. 20E Ch. 0.1 - Prob. 21E Ch. 0.1 - Prob. 22E Ch. 0.1 - Prob. 23E Ch. 0.1 - Prob. 24E Ch. 0.1 - Prob. 25E Ch. 0.1 - Prob. 26E Ch. 0.1 - Prob. 27E Ch. 0.1 - Prob. 28E Ch. 0.1 - Prob. 29E Ch. 0.1 - Prob. 30E Ch. 0.1 - Prob. 31E Ch. 0.1 - Prob. 32E Ch. 0.1 - Prob. 33E Ch. 0.1 - Prob. 34E Ch. 0.1 - Prob. 35E Ch. 0.1 - Prob. 36E Ch. 0.1 - Convert each expression in Exercises 25-50 into...Ch. 0.1 - Prob. 38E Ch. 0.1 - Prob. 39E Ch. 0.1 - Prob. 40E Ch. 0.1 - Prob. 41E Ch. 0.1 - Prob. 42E Ch. 0.1 - Prob. 43E Ch. 0.1 - Prob. 44E Ch. 0.1 - Prob. 45E Ch. 0.1 - Prob. 46E Ch. 0.1 - Prob. 47E Ch. 0.1 - Prob. 48E Ch. 0.1 - Prob. 49E Ch. 0.1 - Prob. 50E Ch. 0.2 - Evaluate the expression sin Exercises 116. 33 Ch. 0.2 - Prob. 2E Ch. 0.2 - Evaluate the expression sin Exercises 116. 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The factors of the expression x 4 − 5 x 2 + 4 .

Solution Summary: The author explains how to calculate the factors of the quadratic equation ax2+bx+c by trial and error method.