Poles and Zeroes - Z Domain 2nd order Butterworth transfer function:

$$H(z) = \frac{ 0.0201z^2 + 0.0402z + 0.0201 } { z^2 - 1.5609z + 0.6413 }$$

I'm a bit uncertain about the factorization at the denominator. Here's what I have so far:

\begin{eqnarray*}
H(z) &amp;=&amp; \frac{ 0.0201(z^2 +2z + 1)  }{ z^2 - 1.5609z + 0.6413 }\\
 &amp;=&amp; \frac{ 0.0201(z + 1)(z + 1)  }{ z(z - 1.5609) + 0.6413 }
\end{eqnarray*}
Zeros : $z + 1 = 0$, zero at $z = -1$.

How can I find the poles?
use the quadratic formula.  you know:

$$ a \, x^2 \ + \ b \, x \ + \ c \ = \ 0 $$

$\implies$

$$ x = \begin{cases}
 \frac{-b \, \pm \sqrt{b^2 - 4 a c}}{2\,a}  \quad \text{if } b^2 \ge 4 a c \\
  \\
 \frac{-b \, \pm j \sqrt{4 a c -b^2}}{2\,a}  \quad \text{if } b^2 &lt; 4 a c\\
\end{cases}$$