Find roots of polynomial $$ p(x) = 2x^3-x^2-7x+6+x^6+x^5-3x^{11} $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 0.9475\\[1 em]x_2 &= 0.581+0.9484i\\[1 em]x_3 &= 0.581-0.9484i\\[1 em]x_4 &= -0.7493+0.8963i\\[1 em]x_5 &= -0.7493-0.8963i\\[1 em]x_6 &= -0.0556+1.1239i\\[1 em]x_7 &= -0.0556-1.1239i\\[1 em]x_8 &= 0.8226+0.3392i\\[1 em]x_9 &= 0.8226-0.3392i\\[1 em]x_{10} &= -1.0725+0.3111i\\[1 em]x_{11} &= -1.0725-0.3111i \end{aligned} $$Explanation
Step 1:
Write polynomial in descending order
$$ \begin{aligned} 2x^3-x^2-7x+6+x^6+x^5-3x^{11} & = 0\\[1 em] -3x^{11}+x^6+x^5+2x^3-x^2-7x+6 & = 0 \end{aligned} $$Step 2:
Polynomial $ -3x^{11}+x^6+x^5+2x^3-x^2-7x+6 $ 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