Find roots of polynomial $$ p(x) = 3-2x^2-4x^3+x^5 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 0.8\\[1 em]x_2 &= -1.8423\\[1 em]x_3 &= 2.1514\\[1 em]x_4 &= -0.5545+0.7992i\\[1 em]x_5 &= -0.5545-0.7992i \end{aligned} $$Explanation
Step 1:
Write polynomial in descending order
$$ \begin{aligned} 3-2x^2-4x^3+x^5 & = 0\\[1 em] x^5-4x^3-2x^2+3 & = 0 \end{aligned} $$Step 2:
Polynomial $ x^5-4x^3-2x^2+3 $ has no rational roots that can be found using Rational Root Test, so the roots were found using Newton method.
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