Find roots of polynomial $$ p(x) = x^3-\frac{1}{2}x^2+4x+2 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= -0.4515\\[1 em]x_2 &= 0.4758+2.0502i\\[1 em]x_3 &= 0.4758-2.0502i \end{aligned} $$Explanation
Step 1:
Get rid of fractions by multipling equation by $ \color{blue}{ 2 } $.
$$ \begin{aligned} x^3-\frac{1}{2}x^2+4x+2 & = 0 ~~~ / \cdot \color{blue}{ 2 } \\[1 em] 2x^3-x^2+8x+4 & = 0 \end{aligned} $$Step 2:
Polynomial $ 2x^3-x^2+8x+4 $ has no rational roots that can be found using Rational Root Test, so the roots were found using qubic formulas.
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