The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 53.3832\\[1 em]x_2 &= 2.1168 \end{aligned} $$The solutions of $ 2x^2-111x+226 = 0 $ are: $ x = \dfrac{ 111 }{ 4 }-\dfrac{\sqrt{ 10513 }}{ 4 } ~ \text{and} ~ x = \dfrac{ 111 }{ 4 }+\dfrac{\sqrt{ 10513 }}{ 4 }$.
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