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Q.17 In the formation of Routh-Hurwitz array for a polynomial, all the elements of a row have zero values. This premature termination of the array indicates the presence of

1. only one root at the origin
2. imaginary roots
3. only positive real roots
4. only negative real roots

Correct answer: imaginary roots

Solution

When a row in the Routh-Hurwitz array consists entirely of zeros, it indicates that the polynomial has roots that are not real, which typically means the presence of imaginary roots. This situation arises because the polynomial's behavior suggests oscillatory characteristics, leading to complex conjugate pairs.

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