Find roots of polynomial $$ p(x) = 5x^4+\frac{416}{100}x^3+\frac{6678}{100}x^2+74x+20 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= -0.4534\\[1 em]x_2 &= -0.6599\\[1 em]x_3 &= 0.1406+3.6538i\\[1 em]x_4 &= 0.1406-3.6538i \end{aligned} $$Explanation
Step 1:
Get rid of fractions by multipling equation by $ \color{blue}{ 100 } $.
$$ \begin{aligned} 5x^4+\frac{416}{100}x^3+\frac{6678}{100}x^2+74x+20 & = 0 ~~~ / \cdot \color{blue}{ 100 } \\[1 em] 500x^4+416x^3+6678x^2+7400x+2000 & = 0 \end{aligned} $$Step 2:
Polynomial $ 500x^4+416x^3+6678x^2+7400x+2000 $ has no rational roots that can be found using Rational Root Test, so the roots were found using quartic formulas.
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