Given the following polynomial equation s^3 + 5.5s^2 + 8.5s + 3 = 0, the number of roots of the polynomial, which have real parts strictly less than - - General SHORT_ANSWER PYQs Based Test - 06 : Control Systems | ExamTest.live

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Given the following polynomial equation s^{3} + 5.5 s^{2} + 8.5 s + 3 = 0, the number of roots of the polynomial, which have real parts strictly less than - 1, is ________

Correct Answer

Solution & Step-by-step Explanation

In the range: 2 - 2 s³+ 5.5s² + 8.5s + 3 = 0 Putting s = z -1 (z - 1)^{3} + 5.5 (z - 1)^{2} + (8.5) (z - 1) + 3 = 0 z³ + 2.5z² + 0.5z - 1 = 1 Taking routh criteria for the given characteristic equation z^{3} 1 0.5 z^{2} 2.5 -1 z 0.9 0 z^{0} -1 As there is one sign change hence, two roots of given polynomial will lie to the left of s = -1.

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Given the following polynomial equation s^{3} + 5.5 s^{2} + 8.5 s + 3 = 0, the number of roots of the polynomial, which have real parts strictly less than - 1, is ________