Find roots of polynomial $$ p(x) = 2x^3+7x^2+14x+\frac{281}{4} $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= -3.9673\\[1 em]x_2 &= 0.2336+2.9663i\\[1 em]x_3 &= 0.2336-2.9663i \end{aligned} $$Explanation
Step 1:
Get rid of fractions by multipling equation by $ \color{blue}{ 4 } $.
$$ \begin{aligned} 2x^3+7x^2+14x+\frac{281}{4} & = 0 ~~~ / \cdot \color{blue}{ 4 } \\[1 em] 8x^3+28x^2+56x+281 & = 0 \end{aligned} $$Step 2:
Polynomial $ 8x^3+28x^2+56x+281 $ has no rational roots that can be found using Rational Root Test, so the roots were found using qubic formulas.
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