Question
Find roots of polynomial $$ p(x) = x^2-\frac{975}{100}-\frac{7}{10}x $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 3.4921\\[1 em]x_2 &= -2.7921 \end{aligned} $$Explanation
Step 1:
Get rid of fractions by multipling equation by $ \color{blue}{ 100 } $.
$$ \begin{aligned} x^2-\frac{975}{100}-\frac{7}{10}x & = 0 ~~~ / \cdot \color{blue}{ 100 } \\[1 em] 100x^2-975-70x & = 0 \end{aligned} $$Step 2:
Write polynomial in descending order
$$ \begin{aligned} 100x^2-975-70x & = 0\\[1 em] 100x^2-70x-975 & = 0 \end{aligned} $$Step 3:
The solutions of $ 100x^2-70x-975 = 0 $ are: $ x = \dfrac{ 7 }{ 20 }-\dfrac{\sqrt{ 3949 }}{ 20 } ~ \text{and} ~ x = \dfrac{ 7 }{ 20 }+\dfrac{\sqrt{ 3949 }}{ 20 }$.
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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