How can I find the poles of a transfer function without using a computer?

[hairy_grape]

Homework Statement

This is an example in the book that I am trying to work.
I am given L(s) = (10(s+10)) / (s(s+3)(s+5))

The transfer function T(s) = 1 / (1+L(s))

Solving for the transfer function I get T(s) = (10(s+10)) / (s^3 + 8s^2 + 25s + 100)

The process of getting the zeros is not shown in the example.

zeros (s+6.5182)(s+.7409+3.8461j)(s+.7409-3.8461j).

I have confirmed the (s+6.5182) in MATLAB then use synthetic division and quadratic formula to get other roots.

My question is how do i get the first root without using MATLAB because we are not allowed to use computers on the test.

thanks,
mike

 

[vela]

You use what you learned back when you studied algebra about how to factor a polynomial, and your instructor would have to give you a problem where you can factor the polynomial by hand. For the example, you've given, you'd need a computer or calculator to find the roots.

By the way, what you're finding are the poles, not the zeros, of the transfer function. The zeros are where the numerator vanishes so T(s)=0. Also, on a side note, the numerator of T(s) you wrote above is incorrect.

 

[hairy_grape]

You use what you learned back when you studied algebra about how to factor a polynomial, and your instructor would have to give you a problem where you can factor the polynomial by hand. For the example, you've given, you'd need a computer or calculator to find the roots.

By the way, what you're finding are the poles, not the zeros, of the transfer function. The zeros are where the numerator vanishes so T(s)=0. Also, on a side note, the numerator of T(s) you wrote above is incorrect.

Yeah you are right. I meant poles of the transfer function/ zeros of the denominator polynomial. And the transfer function should be T(s) = L(s)/(1+L(s)). Apparently I can't type something correct right out of the book lol