Find roots of polynomial $$ p(x) = 4x^7-5x^6+3x^4-5x^2+10 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= -0.9813\\[1 em]x_2 &= 0.577+1.0776i\\[1 em]x_3 &= 0.577-1.0776i\\[1 em]x_4 &= -0.6668+0.786i\\[1 em]x_5 &= -0.6668-0.786i\\[1 em]x_6 &= 1.2055+0.3897i\\[1 em]x_7 &= 1.2055-0.3897i \end{aligned} $$Explanation
Polynomial $ 4x^7-5x^6+3x^4-5x^2+10 $ has no rational roots that can be found using Rational Root Test, so the roots were found using Newton method.
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