Find roots of polynomial $$ p(x) = x^5-\frac{1}{2}x^4-\frac{1}{2}x^3-\frac{1}{2}x^2-2x-6 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 1.8149\\[1 em]x_2 &= 0.4128+1.3536i\\[1 em]x_3 &= 0.4128-1.3536i\\[1 em]x_4 &= -1.0702+0.711i\\[1 em]x_5 &= -1.0702-0.711i \end{aligned} $$Explanation
Step 1:
Get rid of fractions by multipling equation by $ \color{blue}{ 2 } $.
$$ \begin{aligned} x^5-\frac{1}{2}x^4-\frac{1}{2}x^3-\frac{1}{2}x^2-2x-6 & = 0 ~~~ / \cdot \color{blue}{ 2 } \\[1 em] 2x^5-x^4-x^3-x^2-4x-12 & = 0 \end{aligned} $$Step 2:
Polynomial $ 2x^5-x^4-x^3-x^2-4x-12 $ 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