Find roots of polynomial $$ p(x) = 5+12x+3x^2-4x^3+3x^4+x^6 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= -0.63+0.0911i\\[1 em]x_2 &= -0.63-0.0911i\\[1 em]x_3 &= -0.63+2.0911i\\[1 em]x_4 &= -0.63-2.0911i\\[1 em]x_5 &= 1.2599+i\\[1 em]x_6 &= 1.2599-i \end{aligned} $$Explanation
Step 1:
Write polynomial in descending order
$$ \begin{aligned} 5+12x+3x^2-4x^3+3x^4+x^6 & = 0\\[1 em] x^6+3x^4-4x^3+3x^2+12x+5 & = 0 \end{aligned} $$Step 2:
Polynomial $ x^6+3x^4-4x^3+3x^2+12x+5 $ 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