Question

z^4 + z^3 + z^2 + z + 1 as a product of 2 real quadratic factors, z is complex number

Answer 1

\[\rightarrow (z^{2}+az+1)(z^{2}+bz+1)\]
where
a*b = -1
a+b = 1
\[a = \frac{1+\sqrt{5}}{2}\approx1.618\]
\[b = \frac{-2}{1+\sqrt{5}} \approx -0.618\]