Find roots of polynomial $$ p(x) = 3x^9+15x^8+42x^7+90x^6+144x^5-7x^4-35x^3-98x^2-210x-336 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 1.1847\\[1 em]x_2 &= 0.3661+1.1267i\\[1 em]x_3 &= 0.3661-1.1267i\\[1 em]x_4 &= -0.9584+0.6963i\\[1 em]x_5 &= -0.9584-0.6963i\\[1 em]x_6 &= 2.4495i\\[1 em]x_7 &= -2.4495i\\[1 em]x_8 &= -2.5+1.3229i\\[1 em]x_9 &= -2.5-1.3229i \end{aligned} $$Explanation
Polynomial $ 3x^9+15x^8+42x^7+90x^6+144x^5-7x^4-35x^3-98x^2-210x-336 $ has no rational roots that can be found using Rational Root Test, so the roots were found using Newton method.
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