Find roots of polynomial $$ p(x) = 120+120x+60x^2+20x^3+5x^4+x^5 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= -2.1806\\[1 em]x_2 &= -1.6495+1.6939i\\[1 em]x_3 &= -1.6495-1.6939i\\[1 em]x_4 &= 0.2398+3.1283i\\[1 em]x_5 &= 0.2398-3.1283i \end{aligned} $$Explanation
Step 1:
Write polynomial in descending order
$$ \begin{aligned} 120+120x+60x^2+20x^3+5x^4+x^5 & = 0\\[1 em] x^5+5x^4+20x^3+60x^2+120x+120 & = 0 \end{aligned} $$Step 2:
Polynomial $ x^5+5x^4+20x^3+60x^2+120x+120 $ has no rational roots that can be found using Rational Root Test, so the roots were found using Newton method.
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