The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 2.0652\\[1 em]x_2 &= -1.0652 \end{aligned} $$The solutions of $ 5x^2-5x-11 = 0 $ are: $ x = \dfrac{ 1 }{ 2 }-\dfrac{ 7 \sqrt{ 5}}{ 10 } ~ \text{and} ~ x = \dfrac{ 1 }{ 2 }+\dfrac{ 7 \sqrt{ 5}}{ 10 }$.
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