Find roots of polynomial $$ p(x) = 42x^6+12x^5+25x^4+8x^3+21x^2+12x+5 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= -0.365+0.3596i\\[1 em]x_2 &= -0.365-0.3596i\\[1 em]x_3 &= -0.3211+0.7071i\\[1 em]x_4 &= -0.3211-0.7071i\\[1 em]x_5 &= 0.5433+0.6757i\\[1 em]x_6 &= 0.5433-0.6757i \end{aligned} $$Explanation
Polynomial $ 42x^6+12x^5+25x^4+8x^3+21x^2+12x+5 $ has no rational roots that can be found using Rational Root Test, so the roots were found using Newton method.
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