Question
Find roots of polynomial $$ p(x) = \frac{125}{100000}x^2-\frac{14997}{1000}+\frac{100562}{100000}x $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 14.6465\\[1 em]x_2 &= -819.1425 \end{aligned} $$Explanation
Step 1:
Get rid of fractions by multipling equation by $ \color{blue}{ 100000 } $.
$$ \begin{aligned} \frac{125}{100000}x^2-\frac{14997}{1000}+\frac{100562}{100000}x & = 0 ~~~ / \cdot \color{blue}{ 100000 } \\[1 em] 125x^2-1499700+100562x & = 0 \end{aligned} $$Step 2:
Write polynomial in descending order
$$ \begin{aligned} 125x^2-1499700+100562x & = 0\\[1 em] 125x^2+100562x-1499700 & = 0 \end{aligned} $$Step 3:
The solutions of $ 125x^2+100562x-1499700 = 0 $ are: $ x = -\dfrac{ 50281 }{ 125 }-\dfrac{\sqrt{ 2715641461 }}{ 125 } ~ \text{and} ~ x = -\dfrac{ 50281 }{ 125 }+\dfrac{\sqrt{ 2715641461 }}{ 125 }$.
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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