Help with finding roots for transfer functions

[mpm]

I am in a Systems and Vibrations class but am currently doing differential equations.

A problem I am doing requires me to find the transfer function [X(s)/F(s)] and compute the characteristic roots.

So far I have:

X(s)/F(s) = (6s +4)/(s^2+14s+58)

That is the transfer function but now i have to find the roots.

I realize I only concern myself with the s^2+14s+58 part and set it equal to 0.

I can't factor it because of obvious reasons. I tried the quadratic equation but my calculator says its a non-real result which means its complex.

My problem is that I can't figure out how to do the quadratic when there is a complex root.

I know as^2 + bs + c = a[(s + sigma)^2 + omega^2] = 0.

However, I can't figure out how to find the roots using this equation.

Cany anyone help me with this?

Thanks,

Mike

 

[Fermat]

Do you mean that you just want to find the complex roots of the quadratic,

s² + 14s + 58 = 0 ?

Can't you just use the quadratic formula ?