Find roots of polynomial $$ p(x) = 104x^4-188x^3+89x^2-\frac{18279}{100}x+25 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 0.144\\[1 em]x_2 &= 1.8265\\[1 em]x_3 &= -0.0815+0.9524i\\[1 em]x_4 &= -0.0815-0.9524i \end{aligned} $$Explanation
Step 1:
Get rid of fractions by multipling equation by $ \color{blue}{ 100 } $.
$$ \begin{aligned} 104x^4-188x^3+89x^2-\frac{18279}{100}x+25 & = 0 ~~~ / \cdot \color{blue}{ 100 } \\[1 em] 10400x^4-18800x^3+8900x^2-18279x+2500 & = 0 \end{aligned} $$Step 2:
Polynomial $ 10400x^4-18800x^3+8900x^2-18279x+2500 $ has no rational roots that can be found using Rational Root Test, so the roots were found using quartic formulas.
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