Multiple choice

Given the characteristic equation below, select the number of roots which will be located to the right of the imaginary axis s4 + 5s3 - s2 - 17s + 12 = 0.

  1. One

  2. Two

  3. Three

  4. Zero
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Using the Routh-Hurwitz stability criterion, the first column of the Routh array is [1, 5, -1, -17, 12]. There are two sign changes (5 to -1, and -17 to 12), indicating two roots in the right half of the s-plane.

AI explanation

To find the number of roots to the right of the imaginary axis for s^4 + 5s^3 - s^2 - 17s + 12 = 0, we apply the Routh-Hurwitz criterion. The first column of the Routh array for the coefficients is computed as 1, 5, -2/5, -375/2, and 12. Because there are exactly two sign changes in this sequence from 5 to -2/5 and from -375/2 to 12, there are two roots in the right half of the complex plane. The result is Two.

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