Monodromy of the Gauss--Lucas Theorem

$p(z) = z^5 + {}$$\boldsymbol{a_2}$$z^3 + {}$$\boldsymbol{a_3}$$z^2 + {}$$\boldsymbol{a_4}$$z + {}$$\boldsymbol{a_5}$

\(\Large \mathbb{C}_{\text{coeff}}\)
Branch Points
×
$p(z)$
×
$p'(z)$
×
$p''(z)$
×
$p'''(z)$
\(\Large \mathbb{C}_{\text{root}}\)
Click to toggle
$p(z)$
$p'(z)$
$p''(z)$
$p'''(z)$