Fast Way to Find System Poles Without a Calculator?

[Maxwell]

Hey, I was wondering if there is a fast way to find the poles of a system - not using a calculator.

For example,

$$G(s) = \frac {30}{(s^2 + 6s + 20)(s + 2)(s + 13)}$$

I know two poles right off the bat: -2 and -13, but is there a way to get the poles from the quadratic quickly? Besides the using the quadratic equation, I mean.

I don't think there is, but for some reason I thought I saw someone taking the "b" term, in this example 6s, and halving it. So the pole would be 3. I don't think this is right, is it?

Thanks.

 

[FredGarvin]

It's been a really long time since doing controls work for me. However, other than the quadratic formula, your idea of halving the b term seemed to give you the real component of the roots (they are complex roots). You would have to change the sign on the real part as well.

 

[Maxwell]

Well for what I am interested in, I only need the real term. The imaginary part doesn't play a role in figuring out if a system has dominant poles.

Thank you for answering, this will save me much time.