Find roots of polynomial $$ p(x) = 3x^7+2x^6+x^5+5x^4+6x^3-7x^2-8x-9 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 1.0996\\[1 em]x_2 &= -0.3742+0.75i\\[1 em]x_3 &= -0.3742-0.75i\\[1 em]x_4 &= -1.1784+0.6089i\\[1 em]x_5 &= -1.1784-0.6089i\\[1 em]x_6 &= 0.6695+1.3264i\\[1 em]x_7 &= 0.6695-1.3264i \end{aligned} $$Explanation
Polynomial $ 3x^7+2x^6+x^5+5x^4+6x^3-7x^2-8x-9 $ has no rational roots that can be found using Rational Root Test, so the roots were found using Newton method.
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