Find roots of polynomial $$ p(x) = x^7+5x^3+2x+15 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= -1.2084\\[1 em]x_2 &= 0.413+1.2712i\\[1 em]x_3 &= 0.413-1.2712i\\[1 em]x_4 &= -1.1247+1.2237i\\[1 em]x_5 &= -1.1247-1.2237i\\[1 em]x_6 &= 1.3159+0.8853i\\[1 em]x_7 &= 1.3159-0.8853i \end{aligned} $$Explanation
Polynomial $ x^7+5x^3+2x+15 $ has no rational roots that can be found using Rational Root Test, so the roots were found using Newton method.
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