# Polynomial and roots in complex s-plane

Discussion in 'Homework Help' started by shteii01, Feb 14, 2011.

1. ### shteii01 Thread Starter AAC Fanatic!

Feb 19, 2010
3,518
515
I have a polynomial: p1=s^3+2s^2+(K+2)s+7
I did a Routh table, I found values of K for which roots of this polynomial are in the left hand side of the imaginary axis.

Now. The imaginary axis is moved to -2. I need to find range of value of K for which the roots of polynomial lie to the left of -2.

I put s+2 instead of s, my polynomial now looks like this: p2=(s+2)^3+2(s+2)^2+(K+2)(s+2)+7
I worked it out, did Routh table, found values of K.

My question is this. How do I relate the values of K from p2 to p1?

2. ### Georacer Moderator

Nov 25, 2009
5,151
1,266
Can you post the two formulas you found for each K? Maybe we can extract an expression.

3. ### shteii01 Thread Starter AAC Fanatic!

Feb 19, 2010
3,518
515
I went over this with my professor. He ran into the same thing I did. The homework was due today so I already turned it in. Thank you for looking into it.

4. ### Georacer Moderator

Nov 25, 2009
5,151
1,266
Please post your answers, so that the rest of the forum can benefit from them in the future.

(is the use of benefit correct?)