Find roots of polynomial $$ p(x) = p^3+\frac{1}{4}p^2+\frac{4}{10}p+1 $$
Answer
The roots of polynomial $ p(p) $ are:
$$ \begin{aligned}p_1 &= -0.9455\\[1 em]p_2 &= 0.3478+0.9678i\\[1 em]p_3 &= 0.3478-0.9678i \end{aligned} $$Explanation
Step 1:
Get rid of fractions by multipling equation by $ \color{blue}{ 20 } $.
$$ \begin{aligned} p^3+\frac{1}{4}p^2+\frac{4}{10}p+1 & = 0 ~~~ / \cdot \color{blue}{ 20 } \\[1 em] 20p^3+5p^2+8p+20 & = 0 \end{aligned} $$Step 2:
Polynomial $ 20p^3+5p^2+8p+20 $ has no rational roots that can be found using Rational Root Test, so the roots were found using qubic formulas.
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