The characteristic equation s^4 + 2s^3 + 3s^2 + 4s + 5 = 0 describes a control system. Using the Routh-Hurwitz criterion, how many roots lie in the right-half s-plane?

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Electrical Engineering QUESTION #2169

Question 1

The characteristic equation $s^4 + 2s^3 + 3s^2 + 4s + 5 = 0$ describes a control system. Using the Routh-Hurwitz criterion, how many roots lie in the right-half s-plane?

$2$✔️
$0$
$4$
$1$

Correct Answer Explanation

Routh first-column elements are: $1, 2, 1, -6, 5$. There are 2 sign changes (at $-6$ and back to $5$), confirming 2 roots in the RHP and an unstable system.

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