Find roots of polynomial $$ p(x) = 5x^5+2x^2+6x-5 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 0.6243\\[1 em]x_2 &= -0.9045+0.7054i\\[1 em]x_3 &= -0.9045-0.7054i\\[1 em]x_4 &= 0.5924+0.9308i\\[1 em]x_5 &= 0.5924-0.9308i \end{aligned} $$Explanation
Polynomial $ 5x^5+2x^2+6x-5 $ has no rational roots that can be found using Rational Root Test, so the roots were found using Newton method.
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