Find roots of polynomial $$ p(x) = x^3-\frac{9}{10}x-\frac{27}{25} $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 1.3126\\[1 em]x_2 &= -0.6563+0.6262i\\[1 em]x_3 &= -0.6563-0.6262i \end{aligned} $$Explanation
Step 1:
Get rid of fractions by multipling equation by $ \color{blue}{ 50 } $.
$$ \begin{aligned} x^3-\frac{9}{10}x-\frac{27}{25} & = 0 ~~~ / \cdot \color{blue}{ 50 } \\[1 em] 50x^3-45x-54 & = 0 \end{aligned} $$Step 2:
Polynomial $ 50x^3-45x-54 $ has no rational roots that can be found using Rational Root Test, so the roots were found using qubic formulas.
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