The roots of polynomial $ p(z) $ are:
$$ \begin{aligned}z_1 &= -0.382\\[1 em]z_2 &= -2.618 \end{aligned} $$The solutions of $ -z^2-3z-1 = 0 $ are: $ z = -\dfrac{ 3 }{ 2 }-\dfrac{\sqrt{ 5 }}{ 2 } ~ \text{and} ~ z = -\dfrac{ 3 }{ 2 }+\dfrac{\sqrt{ 5 }}{ 2 }$.
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