Mechanical Engineering Exam > Mechanical Engineering Questions > The algebraic equation F (s ) = s5 − 3...
Start Learning for Free
The algebraic equation
F (s ) = s5 − 3s4+ 5s3− 7s2 + 4s + 20 is given F ( s ) = 0 has
- a)a single complex root with the remaining roots being real
- b)one positive real root and four complex roots, all with positive real parts
- c)one negative real root, two imaginary roots, and two roots with positive real parts
- d)once positive real root, two imaginary roots, and two roots with negative real parts
Correct answer is option 'C'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
The algebraic equation F (s ) = s5 − 3s4+ 5s3− 7s2 + 4s +...
we can solve it by making Routh Hurwitz array.
We can replace 1st element of s1 by 10.
If we observe the 1st column, sign is changing two times.
So we have two poles on right half side of imaginary
Axis and 5s2+20=0
So, s =±2j and1 pole on left side of imaginary axis .
Most Upvoted Answer
The algebraic equation F (s ) = s5 − 3s4+ 5s3− 7s2 + 4s +...
Analysis of the Algebraic Equation:
The given algebraic equation is F(s) = s^5 - 3s^4 + 5s^3 + 7s^2 - 4s + 20.
Understanding the Roots of the Equation:
To determine the nature of the roots, we can use the Fundamental Theorem of Algebra, which states that a polynomial equation of degree n has exactly n complex roots, counting multiplicities.
Using the Fundamental Theorem of Algebra:
According to the Fundamental Theorem of Algebra, the given equation F(s) = 0 has a total of 5 roots, considering multiplicities.
Identifying the Real and Imaginary Roots:
To determine the nature of the roots, we need to analyze the coefficients of the polynomial equation.
Coefficients of the Polynomial Equation:
The coefficients of the polynomial equation F(s) = s^5 - 3s^4 + 5s^3 + 7s^2 - 4s + 20 are:
- Coefficient of s^5: 1
- Coefficient of s^4: -3
- Coefficient of s^3: 5
- Coefficient of s^2: 7
- Coefficient of s: -4
- Constant term: 20
Analysis of the Coefficients:
- Since the coefficient of s^5 is positive, there are no negative real roots.
- The constant term (20) is positive, indicating that there are no negative real roots.
Conclusion:
Based on the analysis of the coefficients and the Fundamental Theorem of Algebra, we can conclude that the equation F(s) = 0 has:
- One negative real root (as the coefficient of s^5 is positive)
- Two imaginary roots (as the constant term is positive)
- Two roots with positive real parts (as all other coefficients are positive)
Therefore, the correct answer is option 'C': one negative real root, two imaginary roots, and two roots with positive real parts.
The given algebraic equation is F(s) = s^5 - 3s^4 + 5s^3 + 7s^2 - 4s + 20.
Understanding the Roots of the Equation:
To determine the nature of the roots, we can use the Fundamental Theorem of Algebra, which states that a polynomial equation of degree n has exactly n complex roots, counting multiplicities.
Using the Fundamental Theorem of Algebra:
According to the Fundamental Theorem of Algebra, the given equation F(s) = 0 has a total of 5 roots, considering multiplicities.
Identifying the Real and Imaginary Roots:
To determine the nature of the roots, we need to analyze the coefficients of the polynomial equation.
Coefficients of the Polynomial Equation:
The coefficients of the polynomial equation F(s) = s^5 - 3s^4 + 5s^3 + 7s^2 - 4s + 20 are:
- Coefficient of s^5: 1
- Coefficient of s^4: -3
- Coefficient of s^3: 5
- Coefficient of s^2: 7
- Coefficient of s: -4
- Constant term: 20
Analysis of the Coefficients:
- Since the coefficient of s^5 is positive, there are no negative real roots.
- The constant term (20) is positive, indicating that there are no negative real roots.
Conclusion:
Based on the analysis of the coefficients and the Fundamental Theorem of Algebra, we can conclude that the equation F(s) = 0 has:
- One negative real root (as the coefficient of s^5 is positive)
- Two imaginary roots (as the constant term is positive)
- Two roots with positive real parts (as all other coefficients are positive)
Therefore, the correct answer is option 'C': one negative real root, two imaginary roots, and two roots with positive real parts.
Attention Mechanical Engineering Students!
To make sure you are not studying endlessly, EduRev has designed Mechanical Engineering study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Mechanical Engineering.
|
Explore Courses for Mechanical Engineering exam
|
|
Similar Mechanical Engineering Doubts
Top Courses for Mechanical EngineeringView all
The algebraic equation F (s ) = s5 − 3s4+ 5s3− 7s2 + 4s + 20 is given F ( s ) = 0 has a)a single complex root with the remaining roots being realb)one positive real root and four complex roots, all with positive real partsc)one negative real root, two imaginary roots, and two roots with positive real partsd)once positive real root, two imaginary roots, and two roots with negative real partsCorrect answer is option 'C'. Can you explain this answer?
Question Description
The algebraic equation F (s ) = s5 − 3s4+ 5s3− 7s2 + 4s + 20 is given F ( s ) = 0 has a)a single complex root with the remaining roots being realb)one positive real root and four complex roots, all with positive real partsc)one negative real root, two imaginary roots, and two roots with positive real partsd)once positive real root, two imaginary roots, and two roots with negative real partsCorrect answer is option 'C'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about The algebraic equation F (s ) = s5 − 3s4+ 5s3− 7s2 + 4s + 20 is given F ( s ) = 0 has a)a single complex root with the remaining roots being realb)one positive real root and four complex roots, all with positive real partsc)one negative real root, two imaginary roots, and two roots with positive real partsd)once positive real root, two imaginary roots, and two roots with negative real partsCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The algebraic equation F (s ) = s5 − 3s4+ 5s3− 7s2 + 4s + 20 is given F ( s ) = 0 has a)a single complex root with the remaining roots being realb)one positive real root and four complex roots, all with positive real partsc)one negative real root, two imaginary roots, and two roots with positive real partsd)once positive real root, two imaginary roots, and two roots with negative real partsCorrect answer is option 'C'. Can you explain this answer?.
The algebraic equation F (s ) = s5 − 3s4+ 5s3− 7s2 + 4s + 20 is given F ( s ) = 0 has a)a single complex root with the remaining roots being realb)one positive real root and four complex roots, all with positive real partsc)one negative real root, two imaginary roots, and two roots with positive real partsd)once positive real root, two imaginary roots, and two roots with negative real partsCorrect answer is option 'C'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about The algebraic equation F (s ) = s5 − 3s4+ 5s3− 7s2 + 4s + 20 is given F ( s ) = 0 has a)a single complex root with the remaining roots being realb)one positive real root and four complex roots, all with positive real partsc)one negative real root, two imaginary roots, and two roots with positive real partsd)once positive real root, two imaginary roots, and two roots with negative real partsCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The algebraic equation F (s ) = s5 − 3s4+ 5s3− 7s2 + 4s + 20 is given F ( s ) = 0 has a)a single complex root with the remaining roots being realb)one positive real root and four complex roots, all with positive real partsc)one negative real root, two imaginary roots, and two roots with positive real partsd)once positive real root, two imaginary roots, and two roots with negative real partsCorrect answer is option 'C'. Can you explain this answer?.
Solutions for The algebraic equation F (s ) = s5 − 3s4+ 5s3− 7s2 + 4s + 20 is given F ( s ) = 0 has a)a single complex root with the remaining roots being realb)one positive real root and four complex roots, all with positive real partsc)one negative real root, two imaginary roots, and two roots with positive real partsd)once positive real root, two imaginary roots, and two roots with negative real partsCorrect answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for Mechanical Engineering.
Download more important topics, notes, lectures and mock test series for Mechanical Engineering Exam by signing up for free.
Here you can find the meaning of The algebraic equation F (s ) = s5 − 3s4+ 5s3− 7s2 + 4s + 20 is given F ( s ) = 0 has a)a single complex root with the remaining roots being realb)one positive real root and four complex roots, all with positive real partsc)one negative real root, two imaginary roots, and two roots with positive real partsd)once positive real root, two imaginary roots, and two roots with negative real partsCorrect answer is option 'C'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
The algebraic equation F (s ) = s5 − 3s4+ 5s3− 7s2 + 4s + 20 is given F ( s ) = 0 has a)a single complex root with the remaining roots being realb)one positive real root and four complex roots, all with positive real partsc)one negative real root, two imaginary roots, and two roots with positive real partsd)once positive real root, two imaginary roots, and two roots with negative real partsCorrect answer is option 'C'. Can you explain this answer?, a detailed solution for The algebraic equation F (s ) = s5 − 3s4+ 5s3− 7s2 + 4s + 20 is given F ( s ) = 0 has a)a single complex root with the remaining roots being realb)one positive real root and four complex roots, all with positive real partsc)one negative real root, two imaginary roots, and two roots with positive real partsd)once positive real root, two imaginary roots, and two roots with negative real partsCorrect answer is option 'C'. Can you explain this answer? has been provided alongside types of The algebraic equation F (s ) = s5 − 3s4+ 5s3− 7s2 + 4s + 20 is given F ( s ) = 0 has a)a single complex root with the remaining roots being realb)one positive real root and four complex roots, all with positive real partsc)one negative real root, two imaginary roots, and two roots with positive real partsd)once positive real root, two imaginary roots, and two roots with negative real partsCorrect answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice The algebraic equation F (s ) = s5 − 3s4+ 5s3− 7s2 + 4s + 20 is given F ( s ) = 0 has a)a single complex root with the remaining roots being realb)one positive real root and four complex roots, all with positive real partsc)one negative real root, two imaginary roots, and two roots with positive real partsd)once positive real root, two imaginary roots, and two roots with negative real partsCorrect answer is option 'C'. Can you explain this answer? tests, examples and also practice Mechanical Engineering tests.
|
|
Explore Courses for Mechanical Engineering exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup