Find roots of polynomial $$ p(x) = 4+2x^4+3x^9 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= -1.0969\\[1 em]x_2 &= 0.5484+0.8369i\\[1 em]x_3 &= 0.5484-0.8369i\\[1 em]x_4 &= -0.7305+0.6411i\\[1 em]x_5 &= -0.7305-0.6411i\\[1 em]x_6 &= -0.2286+1.0592i\\[1 em]x_7 &= -0.2286-1.0592i\\[1 em]x_8 &= 0.9591+0.4182i\\[1 em]x_9 &= 0.9591-0.4182i \end{aligned} $$Explanation
Step 1:
Write polynomial in descending order
$$ \begin{aligned} 4+2x^4+3x^9 & = 0\\[1 em] 3x^9+2x^4+4 & = 0 \end{aligned} $$Step 2:
Polynomial $ 3x^9+2x^4+4 $ has no rational roots that can be found using Rational Root Test, so the roots were found using Newton method.
This page was created using
Polynomial Roots Calculator