Find roots of polynomial $$ p(x) = 500x^2-\frac{3661}{5}x+\frac{2329}{10} $$

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

$$ \begin{aligned}x_1 &= 0.9974\\[1 em]x_2 &= 0.467 \end{aligned} $$

Step 1:

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

$$ \begin{aligned} 500x^2-\frac{3661}{5}x+\frac{2329}{10} & = 0 ~~~ / \cdot \color{blue}{ 10 } \\[1 em] 5000x^2-7322x+2329 & = 0 \end{aligned} $$

Step 2:

The solutions of $ 5000x^2-7322x+2329 = 0 $ are: $ x = \dfrac{ 3661 }{ 5000 }-\dfrac{\sqrt{ 1757921 }}{ 5000 } ~ \text{and} ~ x = \dfrac{ 3661 }{ 5000 }+\dfrac{\sqrt{ 1757921 }}{ 5000 }$.

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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