Explanation Given: The value of P ( 3 ) is 15 and zeroes of the cubic polynomial P ( x ) are 3 2 and i . Concept used: Factor theorem: “A polynomial P ( x ) has a factor x − k if and only if P ( k ) = 0 .” Conjugate zeroes theorem: “If P ( x ) is a polynomial function having only real coefficients, and id a + b i is a zero of P ( x ) , then the conjugate a − b i is also a zero of P ( x ) .” Calculation: It is given that zeroes of the cubic polynomial P ( x ) are 3 2 and i . If i is the zero of the polynomial P ( x ) then − i is also the zero of the polynomial P ( x ) because the complex roots always occur in a pair with their conjugate. The polynomial P ( x ) is a cubic polynomial and the three zeroes of P ( x ) are 3 2 , i and − i . As per the factor theorem if 3 2 , i and − i are the roots of the cubic polynomial P ( x ) then ( x − 1 ) , ( x + i ) and ( x − 3 2 ) are the linear factors of the polynomial P ( x ) . Represent the polynomial P ( x ) as a product of three factors. P ( x ) = a ( x − i ) ( x + i ) ( x − 3 2 ) ( a is constant ) = a ( x 2 − i 2 ) ( x − 3 2 )

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ISBN: 9780134696522

Author: HORNSBY, John, Lial, Margaret L., Rockswold, Gary K.

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Chapter 4.4, Problem 4RBC

To determine

The cubic polynomial P(x) with real coefficients for which 32 and i are the zeroes and P(3)=15.

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Chapter 4.4, Problem 3RBC

Chapter 4.4, Problem 5RBC

Chapter 4 Solutions

Graphical Approach To College Algebra

Ch. 4.1 - Use an end behavior diagram , , , or to describe...Ch. 4.1 - Use an end behavior diagram , , , or to describe...Ch. 4.1 - Use an end behavior diagram , , , or to describe...Ch. 4.1 - Use an end behavior diagram , , , or to describe...Ch. 4.1 - Use an end behavior diagram , , , or to describe...Ch. 4.1 - Use an end behavior diagram , , , or to describe...Ch. 4.1 - Use an end behavior diagram , , , or to describe...Ch. 4.1 - Use an end behavior diagram , , , or to describe...Ch. 4.1 - Use an end behavior diagram , , , or to describe...Ch. 4.1 - Prob. 20E Ch. 4.1 - Prob. 21E Ch. 4.1 - Prob. 22E Ch. 4.1 - Prob. 23E Ch. 4.1 - Prob. 24E Ch. 4.1 - Prob. 25E Ch. 4.1 - Prob. 26E Ch. 4.1 - Prob. 27E Ch. 4.1 - Prob. 28E Ch. 4.1 - Prob. 29E Ch. 4.1 - Prob. 30E Ch. 4.1 - Prob. 31E Ch. 4.1 - Prob. 32E Ch. 4.1 - Without using a calculator, match each function in...Ch. 4.1 - Prob. 34E Ch. 4.1 - Without using a calculator, match each function in...Ch. 4.1 - Prob. 36E Ch. 4.1 - Prob. 37E Ch. 4.1 - Prob. 38E Ch. 4.1 - Prob. 39E Ch. 4.1 - Prob. 40E Ch. 4.1 - Prob. 41E Ch. 4.1 - Prob. 42E Ch. 4.1 - Prob. 43E Ch. 4.1 - Prob. 44E Ch. 4.1 - CONCEPT CHECK The graphs below show but not...Ch. 4.1 - Prob. 46E Ch. 4.1 - CONCEPT CHECK The graphs below show y = x3 − 3x2 −...Ch. 4.1 - Prob. 48E Ch. 4.1 - CONCEPT CHECK The graphs below show but not...Ch. 4.1 - Prob. 50E Ch. 4.1 - CONCEPT CHECK The graphs below show y = x3 − 3x2 −...Ch. 4.1 - Prob. 52E Ch. 4.1 - CONCEPT CHECK The graphs below show y = x3 − 3x2 −...Ch. 4.1 - Prob. 54E Ch. 4.1 - Prob. 55E Ch. 4.1 - Prob. 56E Ch. 4.1 - Prob. 57E Ch. 4.1 - Prob. 58E Ch. 4.1 - Prob. 59E Ch. 4.1 - Prob. 60E Ch. 4.1 - Prob. 61E Ch. 4.1 - Prob. 62E Ch. 4.1 - Prob. 63E Ch. 4.1 - Prob. 64E Ch. 4.1 - Prob. 65E Ch. 4.1 - Prob. 66E Ch. 4.1 - Prob. 67E Ch. 4.1 - Prob. 68E Ch. 4.1 - Prob. 69E Ch. 4.1 - Prob. 70E Ch. 4.1 - Prob. 71E Ch. 4.1 - Prob. 72E Ch. 4.1 - Prob. 73E Ch. 4.1 - Prob. 74E Ch. 4.2 - CHECKING ANALYTIC SKILLS Simplify each rational...Ch. 4.2 - CHECKING ANALYTIC SKILLS Simplify each rational...Ch. 4.2 - Prob. 3E Ch. 4.2 - Prob. 4E Ch. 4.2 - CHECKING ANALYTIC SKILLS Simplify each rational...Ch. 4.2 - Prob. 6E Ch. 4.2 - Prob. 7E Ch. 4.2 - Prob. 8E Ch. 4.2 - Use the intermediate value theorem to show that...Ch. 4.2 - Prob. 10E Ch. 4.2 - Prob. 11E Ch. 4.2 - Prob. 12E Ch. 4.2 - Use the intermediate value theorem to show that...Ch. 4.2 - Prob. 14E Ch. 4.2 - Prob. 15E Ch. 4.2 - Prob. 16E Ch. 4.2 - Use the intermediate value theorem to show that...Ch. 4.2 - Prob. 18E Ch. 4.2 - CONCEPT CHECK Suppose that a polynomial function P...Ch. 4.2 - Prob. 20E Ch. 4.2 - Find each quotient when P(x) is divided by the...Ch. 4.2 - Prob. 22E Ch. 4.2 - Prob. 23E Ch. 4.2 - Prob. 24E Ch. 4.2 - Find each quotient when P(x) is divided by the...Ch. 4.2 - Prob. 26E Ch. 4.2 - Prob. 27E Ch. 4.2 - Prob. 28E Ch. 4.2 - Find each quotient when P(x) is divided by the...Ch. 4.2 - Prob. 30E Ch. 4.2 - Prob. 31E Ch. 4.2 - Prob. 32E Ch. 4.2 - Use synthetic substitution to find P(k). k = 3;...Ch. 4.2 - Prob. 34E Ch. 4.2 - Prob. 35E Ch. 4.2 - Prob. 36E Ch. 4.2 - Use synthetic substitution to find P(k). k = 2;...Ch. 4.2 - Prob. 38E Ch. 4.2 - Prob. 39E Ch. 4.2 - Prob. 40E Ch. 4.2 - Use synthetic substitution to find P(k). ; P(x) =...Ch. 4.2 - Prob. 42E Ch. 4.2 - Prob. 43E Ch. 4.2 - Prob. 44E Ch. 4.2 - Use synthetic substitution to determine whether...Ch. 4.2 - Prob. 46E Ch. 4.2 - Prob. 47E Ch. 4.2 - Prob. 48E Ch. 4.2 - Use synthetic substitution to determine whether...Ch. 4.2 - Prob. 50E Ch. 4.2 - Prob. 51E Ch. 4.2 - Prob. 52E Ch. 4.2 - Use synthetic substitution to determine whether...Ch. 4.2 - Prob. 54E Ch. 4.2 - Prob. 55E Ch. 4.2 - Prob. 56E Ch. 4.2 - Prob. 57E Ch. 4.2 - Prob. 58E Ch. 4.2 - Prob. 59E Ch. 4.2 - Prob. 60E Ch. 4.2 - For each polynomial at least one zero is given....Ch. 4.2 - Prob. 62E Ch. 4.2 - For each polynomial at least one zero is given....Ch. 4.2 - Prob. 64E Ch. 4.2 - For each polynomial at least one zero is given....Ch. 4.2 - For each polynomial at least one zero is given....Ch. 4.2 - Prob. 67E Ch. 4.2 - Prob. 68E Ch. 4.2 - For each polynomial at least one zero is given....Ch. 4.2 - Prob. 70E Ch. 4.2 - Prob. 71E Ch. 4.2 - Prob. 72E Ch. 4.2 - Factor P(x) into linear factors given that k is a...Ch. 4.2 - Prob. 74E Ch. 4.2 - Prob. 75E Ch. 4.2 - Prob. 76E Ch. 4.2 - Factor P(x) into linear factors given that k is a...Ch. 4.2 - Prob. 78E Ch. 4.2 - Prob. 79E Ch. 4.2 - Prob. 80E Ch. 4.2 - Divide. Ch. 4.2 - Prob. 82E Ch. 4.2 - Divide. Ch. 4.2 - Prob. 84E Ch. 4.2 - Divide. Ch. 4.2 - Prob. 86E Ch. 4.2 - Prob. 87E Ch. 4.2 - Prob. 88E Ch. 4.2 - Prob. 89E Ch. 4.2 - Prob. 90E Ch. 4.2 - Prob. 91E Ch. 4.2 - Prob. 92E Ch. 4.2 - Prob. 1RBC Ch. 4.2 - Prob. 2RBC Ch. 4.2 - Prob. 3RBC Ch. 4.2 - Prob. 4RBC Ch. 4.2 - Prob. 5RBC Ch. 4.2 - Prob. 6RBC Ch. 4.2 - Prob. 7RBC Ch. 4.2 - Prob. 8RBC Ch. 4.2 - Prob. 9RBC Ch. 4.2 - Prob. 10RBC Ch. 4.3 - CHECKING ANALYTIC SKILLS Find a cubic polynomial...Ch. 4.3 - Prob. 2E Ch. 4.3 - CHECKING ANALYTIC SKILLS Find a cubic polynomial...Ch. 4.3 - Prob. 4E Ch. 4.3 - CHECKING ANALYTIC SKILLS Find a cubic polynomial...Ch. 4.3 - CHECKING ANALYTIC SKILLS Find a cubic polynomial...Ch. 4.3 - CHECKING ANALYTIC SKILLS Find a polynomial...Ch. 4.3 - Prob. 8E Ch. 4.3 - CHECKING ANALYTIC SKILLS Find a polynomial...Ch. 4.3 - Prob. 10E Ch. 4.3 - CHECKING ANALYTIC SKILLS Find a polynomial...Ch. 4.3 - Prob. 12E Ch. 4.3 - One or more zeros are given for each polynomial....Ch. 4.3 - Prob. 14E Ch. 4.3 - One or more zeros are given for each polynomial....Ch. 4.3 - Prob. 16E Ch. 4.3 - One or more zeros are given for each polynomial....Ch. 4.3 - Prob. 18E Ch. 4.3 - Find a polynomial function P(x) having leading...Ch. 4.3 - Prob. 20E Ch. 4.3 - Find a polynomial function P(x) having leading...Ch. 4.3 - Prob. 22E Ch. 4.3 - Find a polynomial function P(x) having leading...Ch. 4.3 - Prob. 24E Ch. 4.3 - Prob. 25E Ch. 4.3 - Prob. 26E Ch. 4.3 - Find a polynomial function P(x) having leading...Ch. 4.3 - Prob. 28E Ch. 4.3 - Prob. 29E Ch. 4.3 - Prob. 30E Ch. 4.3 - Sketch by hand the graph of each function. (You...Ch. 4.3 - Prob. 32E Ch. 4.3 - Sketch by hand the graph of each function. (You...Ch. 4.3 - Prob. 34E Ch. 4.3 - Sketch by hand the graph of each function. (You...Ch. 4.3 - Prob. 36E Ch. 4.3 - Sketch by hand the graph of each function. (You...Ch. 4.3 - Prob. 38E Ch. 4.3 - Prob. 39E Ch. 4.3 - Prob. 40E Ch. 4.3 - CONCEPT CHECK Use the graphs in Exercises 41–46 to...Ch. 4.3 - CONCEPT CHECK Use the graphs in Exercises 41–46 to...Ch. 4.3 - CONCEPT CHECK Use the graphs in Exercises 41–46 to...Ch. 4.3 - Prob. 44E Ch. 4.3 - CONCEPT CHECK Use the graphs in Exercises 41–46 to...Ch. 4.3 - Prob. 46E Ch. 4.3 - Prob. 47E Ch. 4.3 - Prob. 48E Ch. 4.3 - Prob. 49E Ch. 4.3 - Prob. 50E Ch. 4.3 - Prob. 51E Ch. 4.3 - Prob. 52E Ch. 4.3 - For each polynomial function, (a) list all...Ch. 4.3 - Prob. 54E Ch. 4.3 - For each polynomial function, (a) list all...Ch. 4.3 - Prob. 56E Ch. 4.3 - For each polynomial function, (a) list all...Ch. 4.3 - Prob. 58E Ch. 4.3 - Prob. 59E Ch. 4.3 - Prob. 60E Ch. 4.3 - Prob. 61E Ch. 4.3 - Prob. 62E Ch. 4.3 - Prob. 63E Ch. 4.3 - Prob. 64E Ch. 4.3 - Prob. 65E Ch. 4.3 - Prob. 66E Ch. 4.3 - Prob. 67E Ch. 4.3 - Prob. 68E Ch. 4.3 - Prob. 69E Ch. 4.3 - Prob. 70E Ch. 4.3 - Prob. 71E Ch. 4.3 - Prob. 72E Ch. 4.3 - Prob. 73E Ch. 4.3 - Prob. 74E Ch. 4.3 - Prob. 75E Ch. 4.3 - Prob. 76E Ch. 4.3 - Prob. 77E Ch. 4.3 - Prob. 78E Ch. 4.3 - Prob. 79E Ch. 4.3 - Prob. 80E Ch. 4.3 - Prob. 81E Ch. 4.3 - Prob. 82E Ch. 4.3 - Prob. 83E Ch. 4.3 - Prob. 84E Ch. 4.3 - Prob. 85E Ch. 4.3 - Prob. 86E Ch. 4.3 - Prob. 87E Ch. 4.3 - Prob. 88E Ch. 4.3 - Prob. 89E Ch. 4.3 - Prob. 90E Ch. 4.3 - Prob. 91E Ch. 4.3 - Prob. 92E Ch. 4.3 - RELATING CONCEPTS For individual or group...Ch. 4.3 - Prob. 94E Ch. 4.3 - Prob. 95E Ch. 4.3 - do the following in order. Use Descartes’ rule of...Ch. 4.3 - Prob. 97E Ch. 4.3 - Prob. 98E Ch. 4.4 - Prob. 1E Ch. 4.4 - Prob. 2E Ch. 4.4 - Prob. 3E Ch. 4.4 - Prob. 4E Ch. 4.4 - Prob. 5E Ch. 4.4 - Prob. 6E Ch. 4.4 - Prob. 7E Ch. 4.4 - Prob. 8E Ch. 4.4 - CHECKING ANALYTIC SKILLS Find all real solutions....Ch. 4.4 - Prob. 10E Ch. 4.4 - Prob. 11E Ch. 4.4 - Prob. 12E Ch. 4.4 - CHECKING ANALYTIC SKILLS Find all complex...Ch. 4.4 - Prob. 14E Ch. 4.4 - Prob. 15E Ch. 4.4 - Prob. 16E Ch. 4.4 - CHECKING ANALYTIC SKILLS Find all complex...Ch. 4.4 - Prob. 18E Ch. 4.4 - Prob. 19E Ch. 4.4 - Solve each equation analytically for all complex...Ch. 4.4 - Solve each equation analytically for all complex...Ch. 4.4 - Prob. 22E Ch. 4.4 - Prob. 23E Ch. 4.4 - Prob. 24E Ch. 4.4 - Prob. 25E Ch. 4.4 - Prob. 26E Ch. 4.4 - Prob. 27E Ch. 4.4 - Prob. 28E Ch. 4.4 - Prob. 29E Ch. 4.4 - Prob. 30E Ch. 4.4 - Prob. 31E Ch. 4.4 - Prob. 32E Ch. 4.4 - Prob. 33E Ch. 4.4 - Prob. 34E Ch. 4.4 - Prob. 35E Ch. 4.4 - Prob. 36E Ch. 4.4 - Graph each polynomial function by hand, as shown...Ch. 4.4 - Prob. 38E Ch. 4.4 - Graph each polynomial function by hand, as shown...Ch. 4.4 - Prob. 40E Ch. 4.4 - Graph each polynomial function by hand, as shown...Ch. 4.4 - Prob. 42E Ch. 4.4 - Prob. 43E Ch. 4.4 - Prob. 44E Ch. 4.4 - Prob. 45E Ch. 4.4 - Prob. 46E Ch. 4.4 - Prob. 47E Ch. 4.4 - Prob. 48E Ch. 4.4 - Prob. 49E Ch. 4.4 - Prob. 50E Ch. 4.4 - Prob. 51E Ch. 4.4 - Prob. 52E Ch. 4.4 - Prob. 53E Ch. 4.4 - Prob. 54E Ch. 4.4 - Find all n complex solutions of each equation of...Ch. 4.4 - Prob. 56E Ch. 4.4 - Prob. 57E Ch. 4.4 - Prob. 58E Ch. 4.4 - Find all n complex solutions of each equation of...Ch. 4.4 - Prob. 60E Ch. 4.4 - Prob. 61E Ch. 4.4 - Prob. 62E Ch. 4.4 - Find all n complex solutions of each equation of...Ch. 4.4 - Prob. 64E Ch. 4.4 - Prob. 65E Ch. 4.4 - Prob. 66E Ch. 4.4 - Prob. 67E Ch. 4.4 - Prob. 68E Ch. 4.4 - Prob. 69E Ch. 4.4 - Prob. 70E Ch. 4.4 - Prob. 71E Ch. 4.4 - Prob. 72E Ch. 4.4 - Prob. 73E Ch. 4.4 - Prob. 74E Ch. 4.4 - Prob. 75E Ch. 4.4 - Prob. 76E Ch. 4.4 - Prob. 77E Ch. 4.4 - Prob. 78E Ch. 4.4 - Prob. 1RBC Ch. 4.4 - Prob. 2RBC Ch. 4.4 - Prob. 3RBC Ch. 4.4 - Prob. 4RBC Ch. 4.4 - Prob. 5RBC Ch. 4.4 - Prob. 6RBC Ch. 4.4 - Prob. 7RBC Ch. 4.4 - Prob. 8RBC Ch. 4 - Prob. 1RE Ch. 4 - Prob. 2RE Ch. 4 - Prob. 3RE Ch. 4 - Prob. 4RE Ch. 4 - Prob. 5RE Ch. 4 - Prob. 6RE Ch. 4 - Prob. 7RE Ch. 4 - Prob. 8RE Ch. 4 - Prob. 9RE Ch. 4 - Prob. 10RE Ch. 4 - Prob. 11RE Ch. 4 - Prob. 12RE Ch. 4 - Prob. 13RE Ch. 4 - Prob. 14RE Ch. 4 - Prob. 15RE Ch. 4 - Prob. 16RE Ch. 4 - Prob. 17RE Ch. 4 - Prob. 18RE Ch. 4 - Prob. 19RE Ch. 4 - Prob. 20RE Ch. 4 - Prob. 21RE Ch. 4 - Prob. 22RE Ch. 4 - Prob. 23RE Ch. 4 - Prob. 24RE Ch. 4 - Prob. 25RE Ch. 4 - Prob. 26RE Ch. 4 - Prob. 27RE Ch. 4 - Prob. 28RE Ch. 4 - Give the solution set of each inequality, using...Ch. 4 - Prob. 30RE Ch. 4 - Prob. 31RE Ch. 4 - Prob. 32RE Ch. 4 - Prob. 33RE Ch. 4 - Prob. 34RE Ch. 4 - Prob. 35RE Ch. 4 - Prob. 36RE Ch. 4 - Prob. 37RE Ch. 4 - Prob. 38RE Ch. 4 - Prob. 39RE Ch. 4 - Prob. 40RE Ch. 4 - Prob. 41RE Ch. 4 - Prob. 42RE Ch. 4 - Prob. 43RE Ch. 4 - Prob. 44RE Ch. 4 - Prob. 45RE Ch. 4 - Prob. 46RE Ch. 4 - Prob. 47RE Ch. 4 - Prob. 48RE Ch. 4 - Prob. 49RE Ch. 4 - Prob. 50RE Ch. 4 - Prob. 51RE Ch. 4 - Prob. 52RE Ch. 4 - Prob. 53RE Ch. 4 - Prob. 54RE Ch. 4 - Prob. 55RE Ch. 4 - Prob. 56RE Ch. 4 - Prob. 1T Ch. 4 - Prob. 2T Ch. 4 - Consider the function Use a calculator to give a...Ch. 4 - Prob. 4T Ch. 4 - Prob. 5T Ch. 4 - Prob. 6T Ch. 4 - Prob. 7T Ch. 4 - Prob. 8T Ch. 4 - Prob. 9T Ch. 4 - Prob. 10T Ch. 4 - Prob. 11T Ch. 4 - Prob. 12T Ch. 4 - Prob. 13T Ch. 4 - Prob. 14T

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The cubic polynomial P ( x ) with real coefficients for which 3 2 and i are the zeroes and P ( 3 ) = 15 .

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The cubic polynomial P(x) with real coefficients for which 32 and i are the zeroes and P(3)=15.

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Chapter 4 Solutions