Explanation Theorem used: Rational Root Theorem: Any rational root r r of a polynomial equation f ( x ) = a n x n + a n − 1 x n − 1 + ⋯ + a 0 = 0 is an integer factor of a 0 divided by an integer factor of a n . Therefore, r r = integer factor of a 0 integer factor of a n . Definition used: Descartes’ Rule of Signs: The number of positive of a polynomial equation f ( x ) = 0 cannot be greater than the number of changes in sign in f ( x ) in moving from one term to the next in f ( x ) . The number of negative cannot be greater than the number of sign changes in f ( − x ) . Calculation: It is given that the polynomial equation is 2 x 5 + 5 x 4 − 4 x 3 − 19 x 2 − 16 x = 4 . Here, f ( x ) = 2 x 5 + 5 x 4 − 4 x 3 − 19 x 2 − 16 x − 4 and the degree is 5. Move from left to right, obtain the number of sign changes. As there is 1 sign change, the number of positive roots is 1. f ( − x ) = 2 ( − x ) 5 + 5 ( − x ) 4 − 4 ( − x ) 3 − 19 ( − x ) 2 − 16 ( − x ) − 4 = − 2 x 5 + 5 x 4 + 4 x 3 − 19 x 2 + 16 x − 4 As there are 4 sign changes, the number of negative roots is 4. Hence, the maximum possible numbers of positive and negative roots of 2 x 5 + 5 x 4 − 4 x 3 − 19 x 2 − 16 x − 4 = 0 are 1 and 4, respectively. Thus, the possible rational roots by Rational Root Theorem are, r r = integer factor of 4 integer factor of 2 = 1 , 2 , 4 , 1 , 2 = ± 1 , ± 2 , ± 4 , ± 1 2 Begin with − 1 , perform synthetic division as follows. 2 5 − 4 − 19 − 16 − 4 − 2 − 3 7 12 4 2 3 − 7 − 12 − 4 0 [ − 1 ] The remainder is 0

Student Solutions Manual For Basic Technical Mathematics And Basic Technical Mathematics With Calculus

11th Edition

ISBN: 9780134434636

Author: Allyn J. Washington, Richard Evans

Publisher: PEARSON

See similar textbooks

Videos

Question

Chapter 15.3, Problem 20E

To determine

The roots of the equation without the help of calculator.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 15.3, Problem 19E

Chapter 15.3, Problem 21E

Students have asked these similar questions

٣/١ R2X2 2) slots per pole per phase = 3/3 1 B18060 msl Kd 3 Kol Sin (1) 1sin() sin(30) Sin (30) اذا میرید شرح الكتب بس 0 بالفراغ 3) cos (30) 0.866 4) Rotating 5) Synchronous speeds 120*50 G looo 1000-950 1000 50:05 Copper losses: 5kw Rotor input 5 loo kw 0.05 6) 1 اذا ميريد شرح الكتب فقط look 7) rotor DC ined sove in peaper I need a detailed solution on paper please 0 64 (Find the solution of the initial-valued problems: xy' + 2y = x³e* ;y(1) = 0 Q1// Find the solution of: (1) y' + ytqpx = see²x y³

A fluid has density 800 kg/m³ and flows with velocity v = xi + yj + zk, where x, y, and z are measured in meters, and the components of u are measured in meters per second. Find the rate of flow outward through the part of the paraboloid z = 64 - x² - y² that lies above the xy plane.

۳/۱ : +0 العنوان I need a detailed drawing with explanation R₂ = X2 2) slots per pole per phase 3/31 Le msl 180 60 Kd Ka Sin (1) Isin (6) sin(30) Sin (30) اذا ميريد شرح الكتب بس 0 بالفراغ 3) Cos (30) 0.866 4) Rotating 5) Synchronous speed, 120 x 50 S = 1000-950 1000 Copper bosses: 5kw Rotor input 5 6 : loo kw 6) 1 0.05 اذا ميريد شرح الكتب فقط 100 7) rotor DC 1000 ined sove in peaper I need a detailed solution on paper please // Find the solution of: |(2xy³ + 4x)y' = x²y² + y² 351 // Find the solution of: (1) 2xyy' = 1+ y² 01 175 T Τ M

Chapter 15 Solutions

Student Solutions Manual For Basic Technical Mathematics And Basic Technical Mathematics With Calculus

Ch. 15.1 - Use the factor theorem to determine whether t − 2...Ch. 15.1 - Prob. 2PE Ch. 15.1 - Prob. 3PE Ch. 15.1 - Prob. 4PE Ch. 15.1 - Prob. 1E Ch. 15.1 - Prob. 2E Ch. 15.1 - In Exercises 1–4, make the given changes in the...Ch. 15.1 - Prob. 4E Ch. 15.1 - Prob. 5E Ch. 15.1 - Prob. 6E

Ch. 15.1 - Prob. 7E Ch. 15.1 - Prob. 8E Ch. 15.1 - Prob. 9E Ch. 15.1 - Prob. 10E Ch. 15.1 - Prob. 11E Ch. 15.1 - Prob. 12E Ch. 15.1 - Prob. 13E Ch. 15.1 - Prob. 14E Ch. 15.1 - Prob. 15E Ch. 15.1 - Prob. 16E Ch. 15.1 - Prob. 17E Ch. 15.1 - Prob. 18E Ch. 15.1 - Prob. 19E Ch. 15.1 - Prob. 20E Ch. 15.1 - Prob. 21E Ch. 15.1 - Prob. 22E Ch. 15.1 - Prob. 23E Ch. 15.1 - Prob. 24E Ch. 15.1 - Prob. 25E Ch. 15.1 - Prob. 26E Ch. 15.1 - Prob. 27E Ch. 15.1 - Prob. 28E Ch. 15.1 - Prob. 29E Ch. 15.1 - Prob. 30E Ch. 15.1 - Prob. 31E Ch. 15.1 - Prob. 32E Ch. 15.1 - Prob. 33E Ch. 15.1 - Prob. 34E Ch. 15.1 - Prob. 35E Ch. 15.1 - Prob. 36E Ch. 15.1 - Prob. 37E Ch. 15.1 - Prob. 38E Ch. 15.1 - Prob. 39E Ch. 15.1 - Prob. 40E Ch. 15.1 - Prob. 41E Ch. 15.1 - Prob. 42E Ch. 15.1 - Prob. 43E Ch. 15.1 - Prob. 44E Ch. 15.1 - Prob. 45E Ch. 15.1 - Prob. 46E Ch. 15.1 - Prob. 47E Ch. 15.1 - Prob. 48E Ch. 15.1 - Prob. 49E Ch. 15.1 - Prob. 50E Ch. 15.1 - Prob. 51E Ch. 15.1 - Prob. 52E Ch. 15.1 - Prob. 53E Ch. 15.1 - Prob. 54E Ch. 15.1 - Prob. 55E Ch. 15.1 - Prob. 56E Ch. 15.1 - Prob. 57E Ch. 15.1 - Prob. 58E Ch. 15.1 - Prob. 59E Ch. 15.1 - Prob. 60E Ch. 15.2 - Prob. 1PE Ch. 15.2 - Prob. 2PE Ch. 15.2 - Prob. 1E Ch. 15.2 - Prob. 2E Ch. 15.2 - Prob. 3E Ch. 15.2 - Prob. 4E Ch. 15.2 - Prob. 5E Ch. 15.2 - Prob. 6E Ch. 15.2 - Prob. 7E Ch. 15.2 - Prob. 8E Ch. 15.2 - Prob. 9E Ch. 15.2 - Prob. 10E Ch. 15.2 - Prob. 11E Ch. 15.2 - Prob. 12E Ch. 15.2 - Prob. 13E Ch. 15.2 - Prob. 14E Ch. 15.2 - Prob. 15E Ch. 15.2 - Prob. 16E Ch. 15.2 - Prob. 17E Ch. 15.2 - Prob. 18E Ch. 15.2 - Prob. 19E Ch. 15.2 - Prob. 20E Ch. 15.2 - Prob. 21E Ch. 15.2 - Prob. 22E Ch. 15.2 - Prob. 23E Ch. 15.2 - Prob. 24E Ch. 15.2 - Prob. 25E Ch. 15.2 - Prob. 26E Ch. 15.2 - Prob. 27E Ch. 15.2 - Prob. 28E Ch. 15.2 - Prob. 29E Ch. 15.2 - Prob. 30E Ch. 15.2 - Prob. 31E Ch. 15.2 - Prob. 32E Ch. 15.3 - Determine the maximum possible number of positive...Ch. 15.3 - Prob. 2PE Ch. 15.3 - In Exercises 1 and 2, make the given changes in...Ch. 15.3 - Prob. 2E Ch. 15.3 - Prob. 3E Ch. 15.3 - Prob. 4E Ch. 15.3 - Prob. 5E Ch. 15.3 - Prob. 6E Ch. 15.3 - Prob. 7E Ch. 15.3 - Prob. 8E Ch. 15.3 - In Exercises 3–20, solve the given equations...Ch. 15.3 - Prob. 10E Ch. 15.3 - Prob. 11E Ch. 15.3 - Prob. 12E Ch. 15.3 - Prob. 13E Ch. 15.3 - Prob. 14E Ch. 15.3 - Prob. 15E Ch. 15.3 - Prob. 16E Ch. 15.3 - Prob. 17E Ch. 15.3 - Prob. 18E Ch. 15.3 - Prob. 19E Ch. 15.3 - Prob. 20E Ch. 15.3 - Prob. 21E Ch. 15.3 - Prob. 22E Ch. 15.3 - Prob. 23E Ch. 15.3 - Prob. 24E Ch. 15.3 - Prob. 25E Ch. 15.3 - Prob. 26E Ch. 15.3 - Prob. 27E Ch. 15.3 - Prob. 28E Ch. 15.3 - Prob. 29E Ch. 15.3 - Prob. 30E Ch. 15.3 - Prob. 31E Ch. 15.3 - Prob. 32E Ch. 15.3 - Prob. 33E Ch. 15.3 - Prob. 34E Ch. 15.3 - Prob. 35E Ch. 15.3 - Prob. 36E Ch. 15.3 - Prob. 37E Ch. 15.3 - Prob. 38E Ch. 15.3 - Prob. 39E Ch. 15.3 - Prob. 40E Ch. 15.3 - Prob. 41E Ch. 15.3 - Prob. 42E Ch. 15.3 - Prob. 43E Ch. 15.3 - Prob. 44E Ch. 15 - Prob. 1RE Ch. 15 - Prob. 2RE Ch. 15 - Prob. 3RE Ch. 15 - Prob. 4RE Ch. 15 - Prob. 5RE Ch. 15 - Prob. 6RE Ch. 15 - Prob. 7RE Ch. 15 - Prob. 8RE Ch. 15 - Prob. 9RE Ch. 15 - Prob. 10RE Ch. 15 - Prob. 11RE Ch. 15 - Prob. 12RE Ch. 15 - Prob. 13RE Ch. 15 - Prob. 14RE Ch. 15 - Prob. 15RE Ch. 15 - Prob. 16RE Ch. 15 - Prob. 17RE Ch. 15 - Prob. 18RE Ch. 15 - Prob. 19RE Ch. 15 - Prob. 20RE Ch. 15 - Prob. 21RE Ch. 15 - Prob. 22RE Ch. 15 - Prob. 23RE Ch. 15 - Prob. 24RE Ch. 15 - Prob. 25RE Ch. 15 - Prob. 26RE Ch. 15 - Prob. 27RE Ch. 15 - Prob. 28RE Ch. 15 - Prob. 29RE Ch. 15 - Prob. 30RE Ch. 15 - Prob. 31RE Ch. 15 - Prob. 32RE Ch. 15 - Prob. 33RE Ch. 15 - Prob. 34RE Ch. 15 - Prob. 35RE Ch. 15 - Prob. 36RE Ch. 15 - Prob. 37RE Ch. 15 - Prob. 38RE Ch. 15 - Prob. 39RE Ch. 15 - Prob. 40RE Ch. 15 - Prob. 41RE Ch. 15 - Prob. 42RE Ch. 15 - Prob. 43RE Ch. 15 - Prob. 44RE Ch. 15 - Prob. 45RE Ch. 15 - Prob. 46RE Ch. 15 - Prob. 47RE Ch. 15 - Prob. 48RE Ch. 15 - Prob. 49RE Ch. 15 - Prob. 50RE Ch. 15 - Prob. 51RE Ch. 15 - Prob. 52RE Ch. 15 - Prob. 54RE Ch. 15 - Prob. 55RE Ch. 15 - Prob. 56RE Ch. 15 - Prob. 57RE Ch. 15 - Prob. 58RE Ch. 15 - Prob. 59RE Ch. 15 - Prob. 60RE Ch. 15 - Prob. 61RE Ch. 15 - Prob. 62RE Ch. 15 - Prob. 63RE Ch. 15 - Prob. 64RE Ch. 15 - Prob. 65RE Ch. 15 - Prob. 66RE Ch. 15 - Prob. 67RE Ch. 15 - Prob. 68RE Ch. 15 - Prob. 69RE Ch. 15 - Prob. 70RE Ch. 15 - Prob. 71RE Ch. 15 - Prob. 1PT Ch. 15 - Prob. 2PT Ch. 15 - Prob. 3PT Ch. 15 - Prob. 4PT Ch. 15 - Prob. 5PT Ch. 15 - Prob. 6PT Ch. 15 - Prob. 7PT Ch. 15 - Prob. 8PT

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.