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

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

$$ \begin{aligned}x_1 &= 0\\[1 em]x_2 &= \frac{ 25 }{ 6 } \end{aligned} $$

Step 1:

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

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

Step 2:

Write polynomial in descending order

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

Step 3:

Factor out $ \color{blue}{ -16x }$ from $ -96x^2+400x $ and solve two separate equations:

$$ \begin{aligned} -96x^2+400x & = 0\\[1 em] \color{blue}{ -16x }\cdot ( 6x-25 ) & = 0 \\[1 em] \color{blue}{ -16x = 0} ~~ \text{or} ~~ 6x-25 & = 0 \end{aligned} $$

One solution is $ \color{blue}{ x = 0 } $. Use second equation to find the remaining roots.

Step 4:

To find the second zero, solve equation $ 6x-25 = 0 $

$$ \begin{aligned} 6x-25 & = 0 \\[1 em] 6 \cdot x & = 25 \\[1 em] x & = \frac{ 25 }{ 6 } \end{aligned} $$

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