# Positive root solution

• May 22nd 2009, 10:23 AM
Positive root solution
Hi, I've been given the following question for homework.
Determine if the following characteristic equation represents a stable or unstable system.

\$\displaystyle s^3+6s^2+11s+6=0\$

Any tips in solving this would be of great help.
Thanks
• May 22nd 2009, 10:44 AM
Rapha
Hi there

Quote:

Hi, I've been given the following question for homework.
Determine if the following characteristic equation represents a stable or unstable system.

\$\displaystyle s^3+6s^2+11s+6=0\$

Any tips in solving this would be of great help.
Thanks

I found one zero by guessing, it is s=-1. (I know, this is very disappointing, but very fast compared with other methods like http://en.wikipedia.org/wiki/Newton%27s_method or http://en.wikipedia.org/wiki/Cubic_f...ano.27s_method)

Using polynomial long division leads to

\$\displaystyle (s^3+6s^2+11s+6)/(s-(-1)) \$

\$\displaystyle = s^2 + 5s + 6\$

You should be able to find the other two zeros, -3 and -2

All zeros are < 0, therfor I guess (but I don't know) it represents a stable system.

Cheers
Rapha
• May 23rd 2009, 12:49 AM