Find roots of polynomial $$ p(x) = 1+\frac{4}{100}x-\frac{96}{10000}x^2 $$

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

$$ \begin{aligned}x_1 &= \frac{ 25 }{ 2 }\\[1 em]x_2 &= -\frac{ 25 }{ 3 } \end{aligned} $$

Step 1:

Get rid of fractions by multipling equation by $ \color{blue}{ 10000 } $.

$$ \begin{aligned} 1+\frac{4}{100}x-\frac{96}{10000}x^2 & = 0 ~~~ / \cdot \color{blue}{ 10000 } \\[1 em] 10000+400x-96x^2 & = 0 \end{aligned} $$

Step 2:

Write polynomial in descending order

$$ \begin{aligned} 10000+400x-96x^2 & = 0\\[1 em] -96x^2+400x+10000 & = 0 \end{aligned} $$

Step 3:

The solutions of $ -96x^2+400x+10000 = 0 $ are: $ x = -\dfrac{ 25 }{ 3 } ~ \text{and} ~ x = \dfrac{ 25 }{ 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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