Find roots of polynomial $$ p(x) = \frac{22}{10000}x^3-\frac{2913}{10000}x^2+\frac{1173}{100}x-\frac{13764}{100} $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 20.7541\\[1 em]x_2 &= 45.7186\\[1 em]x_3 &= 65.9364 \end{aligned} $$Explanation
Step 1:
Get rid of fractions by multipling equation by $ \color{blue}{ 10000 } $.
$$ \begin{aligned} \frac{22}{10000}x^3-\frac{2913}{10000}x^2+\frac{1173}{100}x-\frac{13764}{100} & = 0 ~~~ / \cdot \color{blue}{ 10000 } \\[1 em] 22x^3-2913x^2+117300x-1376400 & = 0 \end{aligned} $$Step 2:
Polynomial $ 22x^3-2913x^2+117300x-1376400 $ has no rational roots that can be found using Rational Root Test, so the roots were found using qubic formulas.
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