The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 0\\[1 em]x_2 &= \frac{ 1 }{ 3 }+\frac{\sqrt{ 23 }}{ 3 }i\\[1 em]x_3 &= \frac{ 1 }{ 3 }- \frac{\sqrt{ 23 }}{ 3 }i \end{aligned} $$Step 1:
Factor out $ \color{blue}{ x }$ from $ 3x^3-2x^2+8x $ and solve two separate equations:
$$ \begin{aligned} 3x^3-2x^2+8x & = 0\\[1 em] \color{blue}{ x }\cdot ( 3x^2-2x+8 ) & = 0 \\[1 em] \color{blue}{ x = 0} ~~ \text{or} ~~ 3x^2-2x+8 & = 0 \end{aligned} $$One solution is $ \color{blue}{ x = 0 } $. Use second equation to find the remaining roots.
Step 2:
The solutions of $ 3x^2-2x+8 = 0 $ are: $ x = \dfrac{ 1 }{ 3 }+\dfrac{\sqrt{ 23 }}{ 3 }i ~ \text{and} ~ x = \dfrac{ 1 }{ 3 }-\dfrac{\sqrt{ 23 }}{ 3 }i$.
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