Find roots of polynomial $$ p(x) = -3x^2+3x^5+9x^6-4x^4+9 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 0.8739+0.4108i\\[1 em]x_2 &= 0.8739-0.4108i\\[1 em]x_3 &= -0.046+0.9782i\\[1 em]x_4 &= -0.046-0.9782i\\[1 em]x_5 &= -0.9945+0.3597i\\[1 em]x_6 &= -0.9945-0.3597i \end{aligned} $$Explanation
Step 1:
Write polynomial in descending order
$$ \begin{aligned} -3x^2+3x^5+9x^6-4x^4+9 & = 0\\[1 em] 9x^6+3x^5-4x^4-3x^2+9 & = 0 \end{aligned} $$Step 2:
Polynomial $ 9x^6+3x^5-4x^4-3x^2+9 $ 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