For the equation, s3 – 4s2 + s + 6 = 0 the number of roots in the left half ofs-plane will beSelect one:a. Zerob. Onec. Twod. Three

To determine the number of roots in the left half of the s-plane for the 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: | s^3 | s^2 | s^1 | s^0 |

R1 | 1 | -4 | 1 | 6 | R2 | | | | | R3 | | | | |

Step 2: Fill in the first row of the table: | s^3 | s^2 | s^1 | s^0 |

R1 | 1 | -4 | 1 | 6 | R2 | -4 | 6 | | | R3 | | | | |

Step 3: Fill in the second row of the table: | s^3 | s^2 | s^1 | s^0 |

R1 | 1 | -4 | 1 | 6 | R2 | -4 | 6 | | | R3 | 6 | | | |

Step 4: Calculate the remaining elements of the table: | s^3 | s^2 | s^1 | s^0 |

R1 | 1 | -4 | 1 | 6 | R2 | -4 | 6 | 6 | | R3 | 6 | 6 | | |

Step 5: Count the number of sign changes in the first column of the table. In this case, there are 2 sign changes.

Step 6: 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 table. Therefore, the answer is two (c. Two).