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: Calculate the third column of the Routh array:

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

Step 5: Count the number of sign changes in the first column of the Routh array. This will give us the number of roots in the left half of the s-plane.

In this case, there are two sign changes in the first column. Therefore, the number of roots in the left half of the s-plane is two.

So, the answer is (b) Two.