Find roots of polynomial $$ p(x) = x^7+2x^5+1 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= -0.8214\\[1 em]x_2 &= 0.7063+0.4562i\\[1 em]x_3 &= 0.7063-0.4562i\\[1 em]x_4 &= -0.3533+0.848i\\[1 em]x_5 &= -0.3533-0.848i\\[1 em]x_6 &= 0.0577+1.4273i\\[1 em]x_7 &= 0.0577-1.4273i \end{aligned} $$Explanation
Polynomial $ x^7+2x^5+1 $ has no rational roots that can be found using Rational Root Test, so the roots were found using Newton method.
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