Find roots of polynomial $$ p(x) = \frac{2}{27}x^2-\frac{2}{3}x+1 $$

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

$$ \begin{aligned}x_1 &= 7.0981\\[1 em]x_2 &= 1.9019 \end{aligned} $$

Step 1:

Get rid of fractions by multipling equation by $ \color{blue}{ 27 } $.

$$ \begin{aligned} \frac{2}{27}x^2-\frac{2}{3}x+1 & = 0 ~~~ / \cdot \color{blue}{ 27 } \\[1 em] 2x^2-18x+27 & = 0 \end{aligned} $$

Step 2:

The solutions of $ 2x^2-18x+27 = 0 $ are: $ x = \dfrac{ 9 }{ 2 }-\dfrac{ 3 \sqrt{ 3}}{ 2 } ~ \text{and} ~ x = \dfrac{ 9 }{ 2 }+\dfrac{ 3 \sqrt{ 3}}{ 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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