Find roots of polynomial $$ p(x) = -\frac{961}{200}x^2+8x-20 $$

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

$$ \begin{aligned}x_1 &= \frac{ 800 }{ 961 }+\frac{ 60 \sqrt{ 890}}{ 961 }i\\[1 em]x_2 &= \frac{ 800 }{ 961 }-60 \frac{\sqrt{ 890 }}{ 961 }i \end{aligned} $$

Step 1:

Get rid of fractions by multipling equation by $ \color{blue}{ 200 } $.

$$ \begin{aligned} -\frac{961}{200}x^2+8x-20 & = 0 ~~~ / \cdot \color{blue}{ 200 } \\[1 em] -961x^2+1600x-4000 & = 0 \end{aligned} $$

Step 2:

The solutions of $ -961x^2+1600x-4000 = 0 $ are: $ x = \dfrac{ 800 }{ 961 }+\dfrac{ 60 \sqrt{ 890}}{ 961 }i ~ \text{and} ~ x = \dfrac{ 800 }{ 961 }-\dfrac{ 60 \sqrt{ 890}}{ 961 }i$.

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