Explanation Given Information: The provided polynomial equation is ( x 2 − 4 x + 4 ) 2 ( x 2 + 6 x + 5 ) 3 = 0 . Formula used: Principle of zero product rule: An equation a b = 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 The value of x in the equation a x 2 + b x + c = 0 can be given by the quadratic formula, x = − b ± b − 4 a c 2 a where a , b and c are real numbers. Calculation: Consider the polynomial equation ( x 2 − 4 x + 4 ) 2 ( x 2 + 6 x + 5 ) 3 = 0 . Apply the zero-product rule, If ( x 2 − 4 x + 4 ) 2 = 0 Take square root from both sides, x 2 − 4 x + 4 = 0 Compare the above equation with the equation a x 2 + b x + c = 0 , a = 1 , b = − 4 and c = 4 Put the values of a , b , c in the quadratic formula x = − b ± b − 4 a c 2 a

7th Edition

ISBN: 9781337291248

Author: Waner, Stefan.

Publisher: Cengage Learning,

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Chapter 0.5, Problem 44E

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To calculate: The all real solutions in the polynomial equation (x2−4x+4)2(x2+6x+5)3=0.

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Chapter 0.5, Problem 43E

Chapter 0.6, Problem 1E

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For Exercises 115–120, factor the expressions over the set of complex numbers. For assistance, consider these examples. • In Section R.3 we saw that some expressions factor over the set of integers. For example: x - 4 = (x + 2)(x – 2). • Some expressions factor over the set of irrational numbers. For example: - 5 = (x + V5)(x – V5). To factor an expression such as x + 4, we need to factor over the set of complex numbers. For example, verify that x + 4 = (x + 2i)(x – 2i). 115. а. х - 9 116. а. х? - 100 117. а. х - 64 b. x + 9 b. + 100 b. x + 64 118. а. х — 25 119. а. х— 3 120. а. х — 11 b. x + 25 b. x + 3 b. x + 11

Exercises 143–145 will help you prepare for the material covered in the next section. In each exercise, factor completely. 143. 2r + 8x? + 8x 144. 5x3 – 40x?y + 35xy2 145. 96?x + 9b²y – 16x – 16y -

Exercises 86–88 will help you prepare for the material covered in the next section. If –9 is substituted for x in the equation 4x – 3 = 5x + 6, is the resulting statement true or false? Simplify: 13 – 3(x + 2). Зх + Simplify: 10(**1).

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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 all real solutions in the polynomial equation ( x 2 − 4 x + 4 ) 2 ( x 2 + 6 x + 5 ) 3 = 0 .

Solution Summary: The author explains how to calculate the polynomial equation (x2-4x+4) and applies the zero-product rule.

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To calculate: The all real solutions in the polynomial equation (x2−4x+4)2(x2+6x+5)3=0.

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Chapter 0 Solutions