Find roots of polynomial $$ p(x) = 8x^2-\frac{1}{7}x^5+9 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 3.9172\\[1 em]x_2 &= 0.0113+1.0601i\\[1 em]x_3 &= 0.0113-1.0601i\\[1 em]x_4 &= -1.9699+3.2294i\\[1 em]x_5 &= -1.9699-3.2294i \end{aligned} $$Explanation
Step 1:
Get rid of fractions by multipling equation by $ \color{blue}{ 7 } $.
$$ \begin{aligned} 8x^2-\frac{1}{7}x^5+9 & = 0 ~~~ / \cdot \color{blue}{ 7 } \\[1 em] 56x^2-x^5+63 & = 0 \end{aligned} $$Step 2:
Write polynomial in descending order
$$ \begin{aligned} 56x^2-x^5+63 & = 0\\[1 em] -x^5+56x^2+63 & = 0 \end{aligned} $$Step 3:
Polynomial $ -x^5+56x^2+63 $ 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