Find roots of polynomial $$ p(x) = x^2+\frac{2}{3}x-\frac{2}{3} $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 0.5486\\[1 em]x_2 &= -1.2153 \end{aligned} $$Explanation
Step 1:
Get rid of fractions by multipling equation by $ \color{blue}{ 3 } $.
$$ \begin{aligned} x^2+\frac{2}{3}x-\frac{2}{3} & = 0 ~~~ / \cdot \color{blue}{ 3 } \\[1 em] 3x^2+2x-2 & = 0 \end{aligned} $$Step 2:
The solutions of $ 3x^2+2x-2 = 0 $ are: $ x = -\dfrac{ 1 }{ 3 }-\dfrac{\sqrt{ 7 }}{ 3 } ~ \text{and} ~ x = -\dfrac{ 1 }{ 3 }+\dfrac{\sqrt{ 7 }}{ 3 }$.
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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