Find roots of polynomial $$ p(x) = s^2+\frac{49}{10}s+\frac{89}{10} $$

The roots of polynomial $ p(s) $ are:

$$ \begin{aligned}s_1 &= -\frac{ 49 }{ 20 }+\frac{\sqrt{ 1159 }}{ 20 }i\\[1 em]s_2 &= -\frac{ 49 }{ 20 }- \frac{\sqrt{ 1159 }}{ 20 }i \end{aligned} $$

Step 1:

Get rid of fractions by multipling equation by $ \color{blue}{ 10 } $.

$$ \begin{aligned} s^2+\frac{49}{10}s+\frac{89}{10} & = 0 ~~~ / \cdot \color{blue}{ 10 } \\[1 em] 10s^2+49s+89 & = 0 \end{aligned} $$

Step 2:

The solutions of $ 10s^2+49s+89 = 0 $ are: $ s = -\dfrac{ 49 }{ 20 }+\dfrac{\sqrt{ 1159 }}{ 20 }i ~ \text{and} ~ s = -\dfrac{ 49 }{ 20 }-\dfrac{\sqrt{ 1159 }}{ 20 }i$.

You can use step-by-step quadratic equation solver to see a detailed explanation on how to solve this quadratic equation.

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