Find roots of polynomial $$ p(x) = x^3+\frac{144}{10}x^2+\frac{821}{10}x+\frac{1728}{10} $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= -4.7926\\[1 em]x_2 &= -4.8037+3.6028i\\[1 em]x_3 &= -4.8037-3.6028i \end{aligned} $$Explanation
Step 1:
Get rid of fractions by multipling equation by $ \color{blue}{ 10 } $.
$$ \begin{aligned} x^3+\frac{144}{10}x^2+\frac{821}{10}x+\frac{1728}{10} & = 0 ~~~ / \cdot \color{blue}{ 10 } \\[1 em] 10x^3+144x^2+821x+1728 & = 0 \end{aligned} $$Step 2:
Polynomial $ 10x^3+144x^2+821x+1728 $ has no rational roots that can be found using Rational Root Test, so the roots were found using qubic formulas.
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