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