Question
Find roots of polynomial $$ p(x) = 2x^2+\frac{4}{10}x+1 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= -\dfrac{ 1 }{ 10 }+\dfrac{ 7 }{ 10 }i\\[1 em]x_2 &= -\dfrac{ 1 }{ 10 }-\dfrac{ 7 }{ 10 }i \end{aligned} $$Explanation
Step 1:
Get rid of fractions by multipling equation by $ \color{blue}{ 10 } $.
$$ \begin{aligned} 2x^2+\frac{4}{10}x+1 & = 0 ~~~ / \cdot \color{blue}{ 10 } \\[1 em] 20x^2+4x+10 & = 0 \end{aligned} $$Step 2:
The solutions of $ 20x^2+4x+10 = 0 $ are: $ x = -\dfrac{ 1 }{ 10 }+\dfrac{ 7 }{ 10 }i ~ \text{and} ~ x = -\dfrac{ 1 }{ 10 }-\dfrac{ 7 }{ 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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