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Routh Table - Entire row ZERO!

**Entire row is zero**
- If sometimes making a Routh table we find an entire row having zero as there is an even polynomial that is factor of original polynomial.
- It is a different case from the case of zero in first column only. We will see an example how to construct and interpret the Routh table when an entire row is zero.
- Further if the entire row is zero is appeared in Routh table when a purely even or purely odd polynomial is a factor of the original polynomial. Example s4 + 5s2 + 7 are an even polynomial as it has only powers of s.
- Even polynomial only have roots that are in symmetry to the origin. Three conditions can occur .a) roots are symmetrical and real, b)roots are quadrantal, c)roots are symmetric and imaginary.
- Figure 6.5 shows these cases. Each of the cases will generate even polynomial. It is an even polynomial that causes the row of zeros.

- The row of zeros shows the existence of an even polynomial which has roots that are symmetric about the origin. Some of these roots can be on the j?-axis.
- Now however the j? roots are symmetric about the origin, if there are no rows of zeros, we cannot have j? roots.
- Another feature of Routh table is the row previous to the row that of the zero row has an even polynomial which is the factor of the original polynomial.

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