Question
Find roots of polynomial $$ p(x) = -\frac{49}{10}x^2+\frac{2057}{100} $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= \dfrac{ 11 \sqrt{ 170}}{ 70 }\\[1 em]x_2 &= -11 \dfrac{\sqrt{ 170 }}{ 70 } \end{aligned} $$Explanation
Step 1:
Get rid of fractions by multipling equation by $ \color{blue}{ 100 } $.
$$ \begin{aligned} -\frac{49}{10}x^2+\frac{2057}{100} & = 0 ~~~ / \cdot \color{blue}{ 100 } \\[1 em] -490x^2+2057 & = 0 \end{aligned} $$Step 2:
The solutions of $ -490x^2+2057 = 0 $ are: $ x = -11 \dfrac{\sqrt{ 170 }}{ 70 } ~ \text{and} ~ x = \dfrac{ 11 \sqrt{ 170}}{ 70 }$.
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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