Find roots of polynomial $$ p(x) = x^5+5x^4+10x^3+10x^2+5x+5 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= -2.3195\\[1 em]x_2 &= 0.0675+0.7756i\\[1 em]x_3 &= 0.0675-0.7756i\\[1 em]x_4 &= -1.4078+1.2549i\\[1 em]x_5 &= -1.4078-1.2549i \end{aligned} $$Explanation
Polynomial $ x^5+5x^4+10x^3+10x^2+5x+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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