Special Case of Routh Array Case I

Special Case of Routh Array: Case I
Special Case 1
First element of any of the rows of Routh’s Array is zero and remaining same row consists of at-least one non zero element.
The terms in the new row becomes infinity and Routh test fails.

Method 1 :
Substitute a small positive number 𝛆 in place of zero occurred as first element in a row.
Complete the array with this number 𝛆
Then examine the sign change by taking (𝐥𝐢𝐦)┬(𝜺→𝝄)⁡𝑬𝒒𝒖𝒂𝒕𝒊𝒐𝒏

Method 2 :
Replace s by 1/z in the original equation.
Taking the L.C.M rearrange the C.E. descending powers of ‘z’.
Complete the Routh Array with this new equation in ‘z’ and examine the stability.