Find roots of polynomial $$ p(x) = \frac{1}{100}x^3-\frac{1}{4}x^2+\frac{100}{60}x-\frac{100}{68} $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 1.037\\[1 em]x_2 &= 10.6629\\[1 em]x_3 &= 13.3002 \end{aligned} $$Explanation
Step 1:
Get rid of fractions by multipling equation by $ \color{blue}{ 5100 } $.
$$ \begin{aligned} \frac{1}{100}x^3-\frac{1}{4}x^2+\frac{100}{60}x-\frac{100}{68} & = 0 ~~~ / \cdot \color{blue}{ 5100 } \\[1 em] 51x^3-1275x^2+8500x-7500 & = 0 \end{aligned} $$Step 2:
Polynomial $ 51x^3-1275x^2+8500x-7500 $ has no rational roots that can be found using Rational Root Test, so the roots were found using qubic formulas.
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