Find roots of polynomial $$ p(x) = x^2+x+\frac{10}{3} $$

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

$$ \begin{aligned}x_1 &= -\frac{ 1 }{ 2 }+\frac{\sqrt{ 111 }}{ 6 }i\\[1 em]x_2 &= -\frac{ 1 }{ 2 }- \frac{\sqrt{ 111 }}{ 6 }i \end{aligned} $$

Step 1:

Get rid of fractions by multipling equation by $ \color{blue}{ 3 } $.

$$ \begin{aligned} x^2+x+\frac{10}{3} & = 0 ~~~ / \cdot \color{blue}{ 3 } \\[1 em] 3x^2+3x+10 & = 0 \end{aligned} $$

Step 2:

The solutions of $ 3x^2+3x+10 = 0 $ are: $ x = -\dfrac{ 1 }{ 2 }+\dfrac{\sqrt{ 111 }}{ 6 }i ~ \text{and} ~ x = -\dfrac{ 1 }{ 2 }-\dfrac{\sqrt{ 111 }}{ 6 }i$.

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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