The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 342.258\\[1 em]x_2 &= 4.742 \end{aligned} $$The solutions of $ x^2-347x+1623 = 0 $ are: $ x = \dfrac{ 347 }{ 2 }-\dfrac{\sqrt{ 113917 }}{ 2 } ~ \text{and} ~ x = \dfrac{ 347 }{ 2 }+\dfrac{\sqrt{ 113917 }}{ 2 }$.
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