Find roots of polynomial $$ p(x) = 6x^7-15x^6+4x^5+2x^4+7x^3+9x^2+x+12 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= -0.9158\\[1 em]x_2 &= 0.3363+0.7922i\\[1 em]x_3 &= 0.3363-0.7922i\\[1 em]x_4 &= -0.4227+0.835i\\[1 em]x_5 &= -0.4227-0.835i\\[1 em]x_6 &= 1.7943+0.3839i\\[1 em]x_7 &= 1.7943-0.3839i \end{aligned} $$Explanation
Polynomial $ 6x^7-15x^6+4x^5+2x^4+7x^3+9x^2+x+12 $ has no rational roots that can be found using Rational Root Test, so the roots were found using Newton method.
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