Correct AnswerB. Both (A) and (R) are true and (R) is not the correct explanation of (A)
Quick Explanation
Both statements are true: the Routh criterion converts a characteristic polynomial into an algebraic array and is especially convenient for determining the number of right-half-plane roots of higher-order systems without explicitly solving for all roots. However, the second statement is a use of the method rather than the precise reason the array formulation is convenient, so the final-key choice is B.
Detailed Explanation
Concept & Reasoning
Routh-Hurwitz stability analysis uses polynomial coefficients to build the Routh table. Changes of sign in the first column equal the number of roots in the right-half s-plane. It scales well to higher-order characteristic equations compared with direct root calculation, while also handling special zero-row/zero-first-element cases with standard procedures.
How to Solve It in the Exam
Routh table → stability without solving all roots.
Important Exam PointIn assertion-reason questions, distinguish 'both true' from 'R explains A'.
Related Revision Path
This question sits in the revision path Control Systems → Stability → Routh-Hurwitz Criterion .
