Find roots of polynomial $$ p(x) = -\frac{1}{5}x^2+\frac{31}{5}x-\frac{99}{10} $$

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

$$ \begin{aligned}x_1 &= 29.3112\\[1 em]x_2 &= 1.6888 \end{aligned} $$

Step 1:

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

$$ \begin{aligned} -\frac{1}{5}x^2+\frac{31}{5}x-\frac{99}{10} & = 0 ~~~ / \cdot \color{blue}{ 10 } \\[1 em] -2x^2+62x-99 & = 0 \end{aligned} $$

Step 2:

The solutions of $ -2x^2+62x-99 = 0 $ are: $ x = \dfrac{ 31 }{ 2 }-\dfrac{\sqrt{ 763 }}{ 2 } ~ \text{and} ~ x = \dfrac{ 31 }{ 2 }+\dfrac{\sqrt{ 763 }}{ 2 }$.

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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