Find roots of polynomial $$ p(x) = 64x^7+112x^5-56x^3+7x+1 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= -0.2126\\[1 em]x_2 &= -0.2369\\[1 em]x_3 &= -0.5423\\[1 em]x_4 &= 0.4953+0.1328i\\[1 em]x_5 &= 0.4953-0.1328i\\[1 em]x_6 &= 0.0006+1.4749i\\[1 em]x_7 &= 0.0006-1.4749i \end{aligned} $$Explanation
Polynomial $ 64x^7+112x^5-56x^3+7x+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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