Question
Find roots of polynomial $$ p(x) = -3x^3+12x^2-3x $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 0\\[1 em]x_2 &= 3.7321\\[1 em]x_3 &= 0.2679 \end{aligned} $$Explanation
Step 1:
Factor out $ \color{blue}{ -3x }$ from $ -3x^3+12x^2-3x $ and solve two separate equations:
$$ \begin{aligned} -3x^3+12x^2-3x & = 0\\[1 em] \color{blue}{ -3x }\cdot ( x^2-4x+1 ) & = 0 \\[1 em] \color{blue}{ -3x = 0} ~~ \text{or} ~~ x^2-4x+1 & = 0 \end{aligned} $$One solution is $ \color{blue}{ x = 0 } $. Use second equation to find the remaining roots.
Step 2:
The solutions of $ x^2-4x+1 = 0 $ are: $ x = 2-\sqrt{ 3 } ~ \text{and} ~ x = 2+\sqrt{ 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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