All Courses
Explore Courses UPSC Exam UPSC Test Series Free Notes EduRev Infinity Get the App Login Join for Free
Sign in Open App
Electrical Engineering (EE) Exam  >  Electrical Engineering (EE) Questions  >  A system with the polynomials4 + 5s3 + 3s2 + ... Start Learning for Free
SaveJoin the Discussion on the App
A system with the polynomial s4 + 5s3 + 3s2 + 6s + 5 = 0 is:
  • a)
    Unstable
  • b)
    Marginally stable
  • c)
    In equilibrium
  • d)
    Stable
Correct answer is option 'A'. Can you explain this answer?
FREE This question is part of
Download PDF Attempt Test
Download PDF Attempt this Test
Most Upvoted Answer
A system with the polynomials4 + 5s3 + 3s2 + 6s + 5 = 0 is:a)Unstableb...
Explanation:

  • The given polynomial is 4s^3 + 5s^2 + 3s + 5 = 0

  • To determine the stability of the system, we need to analyze the roots of the polynomial.

  • For a polynomial of degree n, there can be n roots.

  • If all the roots have negative real parts, then the system is stable.

  • If all the roots have positive real parts, then the system is unstable.

  • If some roots have positive real parts and some have negative real parts, then the system is marginally stable.



Analysis of the given polynomial:

  • The polynomial has 3 complex roots and no real roots.

  • Complex roots always come in complex conjugate pairs.

  • Therefore, the polynomial has 1 real root and 2 complex conjugate roots.

  • The real root can be positive or negative, but the complex roots always have negative real parts.

  • Therefore, the system is unstable as it has at least one root with a positive real part.



Conclusion:

  • The system with the polynomial 4s^3 + 5s^2 + 3s + 5 = 0 is unstable.

Free Test
FREE
Start Free Test
Start Free Test
Community Answer
A system with the polynomials4 + 5s3 + 3s2 + 6s + 5 = 0 is:a)Unstableb...
The given characteristic equation is: s4 + 5s3 + 3s2 + 6s + 5 = 0. We first need to find the roots by creating the Routh's array table.
Routh's array table is shown below:

In the first column of the above table, we have two sign changes. It means that two roots are in the RHS plane. Hence, the system is unstable.
Hence the correct answer is an option (a).
< Previous Question Next Question >
Explore Courses for Electrical Engineering (EE) exam

Top Courses for Electrical Engineering (EE)View all

Top Courses for Electrical Engineering (EE)

A system with the polynomials4 + 5s3 + 3s2 + 6s + 5 = 0 is:a)Unstableb)Marginally stablec)In equilibriumd)StableCorrect answer is option 'A'. Can you explain this answer?
Question Description
A system with the polynomials4 + 5s3 + 3s2 + 6s + 5 = 0 is:a)Unstableb)Marginally stablec)In equilibriumd)StableCorrect answer is option 'A'. Can you explain this answer? for Electrical Engineering (EE) 2024 is part of Electrical Engineering (EE) preparation. The Question and answers have been prepared according to the Electrical Engineering (EE) exam syllabus. Information about A system with the polynomials4 + 5s3 + 3s2 + 6s + 5 = 0 is:a)Unstableb)Marginally stablec)In equilibriumd)StableCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Electrical Engineering (EE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A system with the polynomials4 + 5s3 + 3s2 + 6s + 5 = 0 is:a)Unstableb)Marginally stablec)In equilibriumd)StableCorrect answer is option 'A'. Can you explain this answer?.
Solutions for A system with the polynomials4 + 5s3 + 3s2 + 6s + 5 = 0 is:a)Unstableb)Marginally stablec)In equilibriumd)StableCorrect answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for Electrical Engineering (EE). Download more important topics, notes, lectures and mock test series for Electrical Engineering (EE) Exam by signing up for free.
Here you can find the meaning of A system with the polynomials4 + 5s3 + 3s2 + 6s + 5 = 0 is:a)Unstableb)Marginally stablec)In equilibriumd)StableCorrect answer is option 'A'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of A system with the polynomials4 + 5s3 + 3s2 + 6s + 5 = 0 is:a)Unstableb)Marginally stablec)In equilibriumd)StableCorrect answer is option 'A'. Can you explain this answer?, a detailed solution for A system with the polynomials4 + 5s3 + 3s2 + 6s + 5 = 0 is:a)Unstableb)Marginally stablec)In equilibriumd)StableCorrect answer is option 'A'. Can you explain this answer? has been provided alongside types of A system with the polynomials4 + 5s3 + 3s2 + 6s + 5 = 0 is:a)Unstableb)Marginally stablec)In equilibriumd)StableCorrect answer is option 'A'. Can you explain this answer? theory, EduRev gives you an ample number of questions to practice A system with the polynomials4 + 5s3 + 3s2 + 6s + 5 = 0 is:a)Unstableb)Marginally stablec)In equilibriumd)StableCorrect answer is option 'A'. Can you explain this answer? tests, examples and also practice Electrical Engineering (EE) tests.
Explore Courses for Electrical Engineering (EE) exam

Top Courses for Electrical Engineering (EE)

Explore Courses

Suggested Free Tests

Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
10M+ students study on EduRev
Get App
© 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