Find roots of polynomial $$ p(x) = -\frac{49}{10}x^2+20x+2 $$

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

$$ \begin{aligned}x_1 &= 4.1793\\[1 em]x_2 &= -0.0977 \end{aligned} $$

Step 1:

Get rid of fractions by multipling equation by $ \color{blue}{ 10 } $.

$$ \begin{aligned} -\frac{49}{10}x^2+20x+2 & = 0 ~~~ / \cdot \color{blue}{ 10 } \\[1 em] -49x^2+200x+20 & = 0 \end{aligned} $$

Step 2:

The solutions of $ -49x^2+200x+20 = 0 $ are: $ x = \dfrac{ 100 }{ 49 }-\dfrac{ 6 \sqrt{ 305}}{ 49 } ~ \text{and} ~ x = \dfrac{ 100 }{ 49 }+\dfrac{ 6 \sqrt{ 305}}{ 49 }$.

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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