The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 1.2965\\[1 em]x_2 &= 0.5785 \end{aligned} $$The solutions of $ 8x^2-15x+6 = 0 $ are: $ x = \dfrac{ 15 }{ 16 }-\dfrac{\sqrt{ 33 }}{ 16 } ~ \text{and} ~ x = \dfrac{ 15 }{ 16 }+\dfrac{\sqrt{ 33 }}{ 16 }$.
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