For the equation, s3 – 4s2 + s + 6 = 0 the number of roots in the left half ofs-plane will beSelect one:a. Threeb. Twoc. Oned. Zero

To determine the number of roots in the left half of the s-plane for the given equation s^3 - 4s^2 + s + 6 = 0, we can use the Routh-Hurwitz stability criterion.

Step 1: Write the coefficients of the equation in a table:

Row 1: 1, 1 Row 2: -4, 6 Row 3: 1

Step 2: Calculate the first column of the Routh array:

Row 1: 1, 1 Row 2: -4, 6 Row 3: 1, 0

Step 3: Calculate the second column of the Routh array:

Row 1: 1, 1 Row 2: -4, 6 Row 3: 1, 0

Step 4: Determine the number of sign changes in the first column. In this case, there are two sign changes.

Step 5: Repeat steps 3 and 4 until the Routh array is complete:

Row 1: 1, 1 Row 2: -4, 6 Row 3: 1, 0

Step 6: Count the number of sign changes in the first column of the completed Routh array. In this case, there is one sign change.

Step 7: The number of roots in the left half of the s-plane is equal to the number of sign changes in the first column of the completed Routh array. Therefore, the answer is one.

So, the correct answer is c. One.