a. Answer Possible rational zeroes of the function are ± 1 , ± 1 2 , ± 2 , ± 4 , ± 8 Explanation Given information: Given function is f ( x ) = − 2 x 4 + 13 x 3 − 21 x 2 + 2 x + 8 Formula used: Rational root test: According to this test, the list of all possible rational zeroes of a polynomial is, Possible zeroes = Factor of constant term Factor of leading coefficient Consider the function as, f ( x ) = − 2 x 4 + 13 x 3 − 21 x 2 + 2 x + 8 Here, leading coefficient is − 2 and constant term is 8 Factors of constant term 8 are ± 1 , ± 2 , ± 4 , ± 8 Factors of leading coefficient − 2 are ± 1 , ± 2 Then possible rational zeroes are, Possible zeroes = ± 1 , ± 2 , ± 4 , ± 8 ± 1 , ± 2 = ± 1 , ± 1 2 , ± 2 , ± 4 , ± 8 Therefore, possible rational zeroes of the function are ± 1 , ± 1 2 , ± 2 , ± 4 , ± 8 b. To determine To draw: The graph of the function f ( x ) = − 2 x 4 + 13 x 3 − 21 x 2 + 2 x + 8 so that some of the possible zeroes in part (a) can be disregarded. Explanation Given information: Given function is f ( x ) = − 2 x 4 + 13 x 3 − 21 x 2 + 2 x + 8 Possible rational zeroes of the function are ± 1 , ± 1 2 , ± 2 , ± 4 , ± 8 Consider the function as f ( x ) = − 2 x 4 + 13 x 3 − 21 x 2 + 2 x + 8 Graph of the function can be drawn as, From the graph of the function, it is clear that zeroes of the function are − 1 2 , 1 , 2 , 4 . c. To determine All the real zeroes of the function f ( x ) = − 2 x 4 + 13 x 3 − 21 x 2 + 2 x + 8 with the help of part (a) and part (b). Answer Real zeroes of the function are x = − 1 2 , 1 , 2 , 4 Explanation Given information: Given function f ( x ) = − 2 x 4 + 13 x 3 − 21 x 2 + 2 x + 8 Possible rational zeroes of the function are ± 1 , ± 1 2 , ± 2 , ± 4 , ± 8 Consider the given function as function f ( x ) = − 2 x 4 + 13 x 3 − 21 x 2 + 2 x + 8 From part (a), possible rational zeroes of the function are ± 1 , ± 1 2 , ± 2 , ± 4 , ± 8 From part (b), it is clear is clear that the curve do not touch x − axis at x = − 1 , 1 2 , − 2 , − 4 , ± 8 Hence, real zeroes of the function are x = − 1 2 , 1 , 2 , 4

4th Edition

ISBN: 9781337516853

Author: Larson

Publisher: CENGAGE CO

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Question

Chapter 2.5, Problem 37E

To determine

To find: The possible rational zeroes of the function f(x)=−2x4+13x3−21x2+2x+8

Expert Solution

Answer to Problem 37E

Possible rational zeroes of the function are ±1,±12,±2,±4,±8

Explanation of Solution

Given information:

Given function is f(x)=−2x4+13x3−21x2+2x+8

Formula used:

Rational root test: According to this test, the list of all possible rational zeroes of a polynomial is,

Possible zeroes =Factor of constant termFactor of leading coefficient

Consider the function as, f(x)=−2x4+13x3−21x2+2x+8

Here, leading coefficient is −2 and constant term is 8

Factors of constant term 8 are ±1,±2,±4,±8

Factors of leading coefficient −2 are ±1,±2

Then possible rational zeroes are,

Possible zeroes=±1,±2,±4,±8±1,±2=±1,±12,±2,±4,±8

Therefore, possible rational zeroes of the function are ±1,±12,±2,±4,±8

To determine

To draw: The graph of the function f(x)=−2x4+13x3−21x2+2x+8 so that some of the possible zeroes in part (a) can be disregarded.

Expert Solution

Explanation of Solution

Given information:

Given function is f(x)=−2x4+13x3−21x2+2x+8

Possible rational zeroes of the function are ±1,±12,±2,±4,±8

Consider the function as f(x)=−2x4+13x3−21x2+2x+8

Graph of the function can be drawn as,

EBK PRECALCULUS W/LIMITS, Chapter 2.5, Problem 37E

From the graph of the function, it is clear that zeroes of the function are −12,1,2,4 .

To determine

All the real zeroes of the function f(x)=−2x4+13x3−21x2+2x+8 with the help of part (a) and part (b).

Expert Solution

Answer to Problem 37E

Real zeroes of the function are x=−12,1,2,4

Explanation of Solution

Given information:

Given function f(x)=−2x4+13x3−21x2+2x+8

Possible rational zeroes of the function are ±1,±12,±2,±4,±8

Consider the given function as function f(x)=−2x4+13x3−21x2+2x+8

From part (a), possible rational zeroes of the function are ±1,±12,±2,±4,±8

From part (b), it is clear is clear that the curve do not touch x − axis at x=−1,12,−2,−4,±8

Hence, real zeroes of the function are x=−12,1,2,4

Chapter 2.5, Problem 36E

Chapter 2.5, Problem 38E

Chapter 2 Solutions

EBK PRECALCULUS W/LIMITS

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Prob. 14E Ch. 2.6 - Prob. 15E Ch. 2.6 - Prob. 16E Ch. 2.6 - Prob. 17E Ch. 2.6 - Prob. 18E Ch. 2.6 - Prob. 19E Ch. 2.6 - Prob. 20E Ch. 2.6 - Prob. 21E Ch. 2.6 - Prob. 22E Ch. 2.6 - Prob. 23E Ch. 2.6 - Prob. 24E Ch. 2.6 - Prob. 25E Ch. 2.6 - Prob. 26E Ch. 2.6 - Prob. 27E Ch. 2.6 - Prob. 28E Ch. 2.6 - Prob. 29E Ch. 2.6 - Prob. 30E Ch. 2.6 - Prob. 31E Ch. 2.6 - Prob. 32E Ch. 2.6 - Prob. 33E Ch. 2.6 - Prob. 34E Ch. 2.6 - Prob. 35E Ch. 2.6 - Prob. 36E Ch. 2.6 - Prob. 37E Ch. 2.6 - Prob. 38E Ch. 2.6 - Prob. 39E Ch. 2.6 - Prob. 40E Ch. 2.6 - Prob. 41E Ch. 2.6 - Prob. 42E Ch. 2.6 - Prob. 43E Ch. 2.6 - Prob. 44E Ch. 2.6 - Prob. 45E Ch. 2.6 - Prob. 46E Ch. 2.6 - Prob. 47E Ch. 2.6 - Prob. 48E Ch. 2.6 - Prob. 49E Ch. 2.6 - Prob. 50E Ch. 2.6 - Prob. 51E Ch. 2.6 - Prob. 52E Ch. 2.6 - Prob. 53E Ch. 2.6 - Prob. 54E Ch. 2.6 - Prob. 55E Ch. 2.6 - Prob. 56E Ch. 2.6 - Prob. 57E Ch. 2.6 - Prob. 58E Ch. 2.6 - Prob. 59E Ch. 2.6 - Prob. 60E Ch. 2.6 - Prob. 61E Ch. 2.6 - Prob. 62E Ch. 2.6 - Prob. 63E Ch. 2.6 - Prob. 64E Ch. 2.6 - Prob. 65E Ch. 2.6 - Prob. 66E Ch. 2.6 - Prob. 67E Ch. 2.6 - Prob. 68E Ch. 2.6 - Prob. 69E Ch. 2.6 - Prob. 70E Ch. 2.6 - Prob. 71E Ch. 2.6 - Prob. 72E Ch. 2.6 - Prob. 73E Ch. 2.6 - Prob. 74E Ch. 2.6 - Prob. 75E Ch. 2.6 - Prob. 76E Ch. 2.6 - Prob. 77E Ch. 2.6 - Prob. 78E Ch. 2.6 - Prob. 79E Ch. 2.6 - Prob. 80E Ch. 2.6 - Prob. 81E Ch. 2.6 - Prob. 82E Ch. 2.7 - Prob. 1E Ch. 2.7 - Prob. 2E Ch. 2.7 - Prob. 3E Ch. 2.7 - Prob. 4E Ch. 2.7 - Prob. 5E Ch. 2.7 - Prob. 6E Ch. 2.7 - Prob. 7E Ch. 2.7 - Prob. 8E Ch. 2.7 - Prob. 9E Ch. 2.7 - Prob. 10E Ch. 2.7 - Prob. 11E Ch. 2.7 - Prob. 12E Ch. 2.7 - Prob. 13E Ch. 2.7 - Prob. 14E Ch. 2.7 - Prob. 15E Ch. 2.7 - Prob. 16E Ch. 2.7 - Prob. 17E Ch. 2.7 - Prob. 18E Ch. 2.7 - Prob. 19E Ch. 2.7 - Prob. 20E Ch. 2.7 - Prob. 21E Ch. 2.7 - Prob. 22E Ch. 2.7 - Prob. 23E Ch. 2.7 - Prob. 24E Ch. 2.7 - Prob. 25E Ch. 2.7 - Prob. 26E Ch. 2.7 - Prob. 27E Ch. 2.7 - Prob. 28E Ch. 2.7 - Prob. 29E Ch. 2.7 - Prob. 30E Ch. 2.7 - Prob. 31E Ch. 2.7 - Prob. 32E Ch. 2.7 - Prob. 33E Ch. 2.7 - Prob. 34E Ch. 2.7 - Prob. 35E Ch. 2.7 - Prob. 36E Ch. 2.7 - Prob. 37E Ch. 2.7 - Prob. 38E Ch. 2.7 - Prob. 39E Ch. 2.7 - Prob. 40E Ch. 2.7 - Prob. 41E Ch. 2.7 - Prob. 42E Ch. 2.7 - Prob. 43E Ch. 2.7 - Prob. 44E Ch. 2.7 - Prob. 45E Ch. 2.7 - Prob. 46E Ch. 2.7 - Prob. 47E Ch. 2.7 - Prob. 48E Ch. 2.7 - Prob. 49E Ch. 2.7 - Prob. 50E Ch. 2.7 - Prob. 51E Ch. 2.7 - Prob. 52E Ch. 2.7 - Prob. 53E Ch. 2.7 - Prob. 54E Ch. 2.7 - Prob. 55E Ch. 2.7 - Prob. 56E Ch. 2.7 - Prob. 57E Ch. 2.7 - Prob. 58E Ch. 2.7 - Prob. 59E Ch. 2.7 - Prob. 60E Ch. 2.7 - Prob. 61E Ch. 2.7 - Prob. 62E Ch. 2.7 - Prob. 63E Ch. 2.7 - Prob. 64E Ch. 2.7 - Prob. 65E Ch. 2.7 - Prob. 66E Ch. 2.7 - Prob. 67E Ch. 2.7 - Prob. 68E Ch. 2.7 - Prob. 69E Ch. 2.7 - Prob. 70E Ch. 2.7 - Prob. 71E Ch. 2.7 - Prob. 72E Ch. 2.7 - Prob. 73E Ch. 2.7 - Prob. 74E Ch. 2.7 - Prob. 75E Ch. 2.7 - Prob. 76E Ch. 2.7 - Prob. 77E Ch. 2.7 - Prob. 78E Ch. 2.7 - Prob. 79E Ch. 2.7 - Prob. 80E Ch. 2.7 - Prob. 81E Ch. 2.7 - Prob. 82E Ch. 2.7 - Prob. 83E Ch. 2.7 - Prob. 84E Ch. 2.7 - Prob. 85E Ch. 2.7 - Prob. 86E Ch. 2.7 - Prob. 87E Ch. 2.7 - Prob. 88E Ch. 2.7 - Prob. 89E Ch. 2.7 - Prob. 90E Ch. 2 - Prob. 1RE Ch. 2 - Prob. 2RE Ch. 2 - Prob. 3RE Ch. 2 - Prob. 4RE Ch. 2 - Prob. 5RE Ch. 2 - Prob. 6RE Ch. 2 - Prob. 7RE Ch. 2 - Prob. 8RE Ch. 2 - Prob. 9RE Ch. 2 - Prob. 10RE Ch. 2 - Prob. 11RE Ch. 2 - Prob. 12RE Ch. 2 - Prob. 13RE Ch. 2 - Prob. 14RE Ch. 2 - Prob. 15RE Ch. 2 - Prob. 16RE Ch. 2 - Prob. 17RE Ch. 2 - Prob. 18RE Ch. 2 - Prob. 19RE Ch. 2 - Prob. 20RE Ch. 2 - Prob. 21RE Ch. 2 - Prob. 22RE Ch. 2 - Prob. 23RE Ch. 2 - Prob. 24RE Ch. 2 - Prob. 25RE Ch. 2 - Prob. 26RE Ch. 2 - Prob. 27RE Ch. 2 - Prob. 28RE Ch. 2 - Prob. 29RE Ch. 2 - Prob. 30RE Ch. 2 - Prob. 31RE Ch. 2 - Prob. 32RE Ch. 2 - Prob. 33RE Ch. 2 - Prob. 34RE Ch. 2 - Prob. 35RE Ch. 2 - Prob. 36RE Ch. 2 - Prob. 37RE Ch. 2 - Prob. 38RE Ch. 2 - Prob. 39RE Ch. 2 - Prob. 40RE Ch. 2 - Prob. 41RE Ch. 2 - Prob. 42RE Ch. 2 - Prob. 43RE Ch. 2 - Prob. 44RE Ch. 2 - Prob. 45RE Ch. 2 - Prob. 46RE Ch. 2 - Prob. 47RE Ch. 2 - Prob. 48RE Ch. 2 - Prob. 49RE Ch. 2 - Prob. 50RE Ch. 2 - Prob. 51RE Ch. 2 - Prob. 52RE Ch. 2 - Prob. 53RE Ch. 2 - Prob. 54RE Ch. 2 - Prob. 55RE Ch. 2 - Prob. 56RE Ch. 2 - Prob. 57RE Ch. 2 - Prob. 58RE Ch. 2 - Prob. 59RE Ch. 2 - Prob. 60RE Ch. 2 - Prob. 61RE Ch. 2 - Prob. 62RE Ch. 2 - Prob. 63RE Ch. 2 - Prob. 64RE Ch. 2 - Prob. 65RE Ch. 2 - Prob. 66RE Ch. 2 - Prob. 67RE Ch. 2 - Prob. 68RE Ch. 2 - Prob. 1CT Ch. 2 - Prob. 2CT Ch. 2 - Prob. 3CT Ch. 2 - Prob. 4CT Ch. 2 - Prob. 5CT Ch. 2 - Prob. 6CT Ch. 2 - Prob. 7CT Ch. 2 - Prob. 8CT Ch. 2 - Prob. 9CT Ch. 2 - Prob. 10CT Ch. 2 - Prob. 11CT Ch. 2 - Prob. 12CT Ch. 2 - Prob. 13CT Ch. 2 - Prob. 14CT Ch. 2 - Prob. 15CT Ch. 2 - Prob. 16CT Ch. 2 - Prob. 17CT Ch. 2 - Prob. 18CT Ch. 2 - Prob. 1PS Ch. 2 - Prob. 2PS Ch. 2 - Prob. 3PS Ch. 2 - Prob. 4PS Ch. 2 - Prob. 5PS Ch. 2 - Prob. 6PS Ch. 2 - Prob. 7PS Ch. 2 - Prob. 8PS Ch. 2 - Prob. 9PS Ch. 2 - Prob. 10PS Ch. 2 - Prob. 11PS Ch. 2 - Prob. 12PS Ch. 2 - Prob. 13PS

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