Mathematics · Control Systems
A polynomial ψ(s) = ansn + an-1sn-1 + ... + a1s + a0 of degree n > 3 with constant real coefficients has a triple root at s = -σ. Which one of the following conditions must be satisfied at s = -σ?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1ψ(s) = 0 and d3ψ(s)/ds3 = 0
- 2ψ(s) = 0, d2ψ(s)/ds2 = 0, and d4ψ(s)/ds4 = 0
- 3ψ(s) = 0, dψ(s)/ds = 0, and d2ψ(s)/ds2 = 0✓
- 4ψ(s) = 0 at all the three values of s satisfying s3 + σ3 = 0
Correct answer
ψ(s) = 0, dψ(s)/ds = 0, and d2ψ(s)/ds2 = 0
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