# Math Help - Positive root solution

1. ## 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.

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

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

2. Hi there

Originally Posted by ady72
Hi, I've been given the following question for homework.
Determine if the following characteristic equation represents a stable or unstable system.

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

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

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

$= s^2 + 5s + 6$

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

3. Thanks Rapha, that has helped meno end.
Cheers