Find roots of polynomial $$ p(x) = -\frac{105}{1000}-\frac{15}{10}x^2+\frac{86}{100}x+x^3 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 0.1638\\[1 em]x_2 &= 0.6681+0.4414i\\[1 em]x_3 &= 0.6681-0.4414i \end{aligned} $$Explanation
Step 1:
Get rid of fractions by multipling equation by $ \color{blue}{ 1000 } $.
$$ \begin{aligned} -\frac{105}{1000}-\frac{15}{10}x^2+\frac{86}{100}x+x^3 & = 0 ~~~ / \cdot \color{blue}{ 1000 } \\[1 em] -105-1500x^2+860x+1000x^3 & = 0 \end{aligned} $$Step 2:
Write polynomial in descending order
$$ \begin{aligned} -105-1500x^2+860x+1000x^3 & = 0\\[1 em] 1000x^3-1500x^2+860x-105 & = 0 \end{aligned} $$Step 3:
Polynomial $ 1000x^3-1500x^2+860x-105 $ has no rational roots that can be found using Rational Root Test, so the roots were found using qubic formulas.
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