Find roots of polynomial $$ p(x) = -x^3+\frac{1}{12}x+\frac{1}{18} $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 0.4537\\[1 em]x_2 &= -0.2268+0.2665i\\[1 em]x_3 &= -0.2268-0.2665i \end{aligned} $$Explanation
Step 1:
Get rid of fractions by multipling equation by $ \color{blue}{ 36 } $.
$$ \begin{aligned} -x^3+\frac{1}{12}x+\frac{1}{18} & = 0 ~~~ / \cdot \color{blue}{ 36 } \\[1 em] -36x^3+3x+2 & = 0 \end{aligned} $$Step 2:
Polynomial $ -36x^3+3x+2 $ has no rational roots that can be found using Rational Root Test, so the roots were found using qubic formulas.
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