why do I suddenly get a gain value in my transfer function?

this is my transfer function:

x=s/[(2*s^2)+(3*s)+1]

when I tried to obtained the zeros and poles value by using zpk function suddenly I got a gain value.

any advice will be much appreciated. thank you in advance

Answer 1

[Jon]

Your original expression and the one found by zpk are the same. zpk just factored out the 2 from denominator.

[Jon]

Note that 1/(2s^2 + 3s + 1) = 1/(2*(s^2 + 1.5s + 0.5), which equals, 0.5/(s^2 + 1.5s + 0.5). So you also have a gain of 0.5 in your original expession

[Matt Mad]

Thanks. My mistake I didn't noticed that