# What is the zero in this transfer function?

What is the zero for the following transfer function, $$-1/2$$ or $$-2$$?

$$H(s) = \frac{2s +1}{(s + 3)(s + 2)}$$

This appears to give a zero of $$-1/2$$.

I can transform this into the standard form that includes the gain $$K$$:

$$H(s) = \frac 12 \left(\frac{s + 2}{(s + 3)(s + 2)}\right)$$

Where the leading half is the gain. The zero now appears to be $$-2$$. What is the conceptual error I am making? Should I take the gain out or leave it in the numerator?

UPDATE: I think this question is worthy of deletion given the nature of the error but I am unable to. Instead, see my answer below.

• sometimes a “dumb questions” can be instructive
– user28715
Commented Mar 2, 2019 at 0:54

$$2s+1=2\left(s+\frac12\right)$$ That's all I can say.

• Oops, I think I’ll delete the question. Commented Mar 1, 2019 at 19:05

Anyone with a brain will realize I made an extremely elementary arithmetic error in my question. The transformed equation should of course be:

which means the zero is -1/2 as expected. The bottom line is that a gain has no effect on the values of the zeros since it is just a scaling factor in the zero polynomial.