The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 14\\[1 em]x_2 &= \frac{ 25 }{ 2 } \end{aligned} $$The solutions of $ 2x^2-53x+350 = 0 $ are: $ x = \dfrac{ 25 }{ 2 } ~ \text{and} ~ x = 14$.
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