Find roots of polynomial $$ p(x) = 92+9x^5-9x^2-x^4-12x^3 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= -1.6636\\[1 em]x_2 &= 1.4608+0.7261i\\[1 em]x_3 &= 1.4608-0.7261i\\[1 em]x_4 &= -0.5735+1.4071i\\[1 em]x_5 &= -0.5735-1.4071i \end{aligned} $$Explanation
Step 1:
Write polynomial in descending order
$$ \begin{aligned} 92+9x^5-9x^2-x^4-12x^3 & = 0\\[1 em] 9x^5-x^4-12x^3-9x^2+92 & = 0 \end{aligned} $$Step 2:
Polynomial $ 9x^5-x^4-12x^3-9x^2+92 $ has no rational roots that can be found using Rational Root Test, so the roots were found using Newton method.
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