Find roots of polynomial $$ p(x) = 7x^6+12x^5+5x^4+8x^3+6x^2-6x-3 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 0.6294\\[1 em]x_2 &= -0.4167\\[1 em]x_3 &= 0.2473+1.0215i\\[1 em]x_4 &= 0.2473-1.0215i\\[1 em]x_5 &= -1.2107+0.1159i\\[1 em]x_6 &= -1.2107-0.1159i \end{aligned} $$Explanation
Polynomial $ 7x^6+12x^5+5x^4+8x^3+6x^2-6x-3 $ has no rational roots that can be found using Rational Root Test, so the roots were found using Newton method.
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