Question
Find roots of polynomial $$ p(x) = 2x^2-8x+\frac{10}{4} $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 3.6583\\[1 em]x_2 &= 0.3417 \end{aligned} $$Explanation
Step 1:
Get rid of fractions by multipling equation by $ \color{blue}{ 4 } $.
$$ \begin{aligned} 2x^2-8x+\frac{10}{4} & = 0 ~~~ / \cdot \color{blue}{ 4 } \\[1 em] 8x^2-32x+10 & = 0 \end{aligned} $$Step 2:
The solutions of $ 8x^2-32x+10 = 0 $ are: $ x = 2-\dfrac{\sqrt{ 11 }}{ 2 } ~ \text{and} ~ x = 2+\dfrac{\sqrt{ 11 }}{ 2 }$.
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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