Question
Find roots of polynomial $$ p(x) = 675s^2+\frac{13616}{10}s+\frac{545245}{100} $$
Answer
The roots of polynomial $ p(s) $ are:
$$ \begin{aligned}s_1 &= -\dfrac{ 3404 }{ 3375 }+\dfrac{\sqrt{ 321691511 }}{ 6750 }i\\[1 em]s_2 &= -\dfrac{ 3404 }{ 3375 }- \dfrac{\sqrt{ 321691511 }}{ 6750 }i \end{aligned} $$Explanation
Step 1:
Get rid of fractions by multipling equation by $ \color{blue}{ 100 } $.
$$ \begin{aligned} 675s^2+\frac{13616}{10}s+\frac{545245}{100} & = 0 ~~~ / \cdot \color{blue}{ 100 } \\[1 em] 67500s^2+136160s+545245 & = 0 \end{aligned} $$Step 2:
The solutions of $ 67500s^2+136160s+545245 = 0 $ are: $ s = -\dfrac{ 3404 }{ 3375 }+\dfrac{\sqrt{ 321691511 }}{ 6750 }i ~ \text{and} ~ s = -\dfrac{ 3404 }{ 3375 }-\dfrac{\sqrt{ 321691511 }}{ 6750 }i$.
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