Explanation Given Information: The equations are: p + q = − 1 And p q = − 12 Formula used: Use the zero-product rule to simplify the factors: ( a − b ) ( b − c ) = 0 Then a − b = 0 or b - c = 0 . Calculation: Consider the linear equations, p + q = − 1 …… ( 1 ) And p q = − 12 …… ( 2 ) Simplify the equation, ( 1 ) , in terms of p : p = − q − 1 …… ( 3 ) Now substitute the value of p = − q − 1 in equation, ( 2 ) , and solve it. p q = − 12 ( − q − 1 ) q = − 12 ( − q 2 − q ) = − 12 − q 2 − q + 12 = 0 Further, simplify, q 2 + q − 12 = 0 ( q + 4 ) ( q − 3 ) = 0 Now simplify both the factors using zero-product rule, q + 4 = 0 q = − 4 And q − 3 = 0 q = 3 Now substitute q = − 4 in the equation, ( 3 ) , and solve for p : p = − q − 1 = − ( − 4 ) − 1 = 3 The ordered pair is ( 3 , − 4 ) . Now substitute q = 3 in the equation, ( 3 ) , and solve for p : p = − q − 1 = − ( 3 ) − 1 = − 4 The ordered pair is ( − 4 , 3 )

Elementary and Intermediate Algebra: Concepts and Applications (7th Edition)

7th Edition

ISBN: 9780134462707

Author: Marvin L. Bittinger, David J. Ellenbogen, Barbara L. Johnson

Publisher: PEARSON

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Chapter 13.4, Problem 22ES

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To calculate: The solution of the equations p+q=−1, pq=−12.

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Chapter 13.4, Problem 21ES

Chapter 13.4, Problem 23ES

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Chapter 13 Solutions

Elementary and Intermediate Algebra: Concepts and Applications (7th Edition)

Ch. 13.1 - Prob. 1YT Ch. 13.1 - Prob. 2YT Ch. 13.1 - Prob. 3YT Ch. 13.1 - Prob. 4YT Ch. 13.1 - Prob. 5YT Ch. 13.1 - Prob. 1CYU Ch. 13.1 - Prob. 2CYU Ch. 13.1 - Prob. 3CYU Ch. 13.1 - Prob. 4CYU Ch. 13.1 - Prob. 5CYU

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The solution of the equations p + q = − 1 , p q = − 12.

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