Question
Find roots of polynomial $$ p(x) = 6x^3-25x^2+2x $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 0\\[1 em]x_2 &= 4.0851\\[1 em]x_3 &= 0.0816 \end{aligned} $$Explanation
Step 1:
Factor out $ \color{blue}{ x }$ from $ 6x^3-25x^2+2x $ and solve two separate equations:
$$ \begin{aligned} 6x^3-25x^2+2x & = 0\\[1 em] \color{blue}{ x }\cdot ( 6x^2-25x+2 ) & = 0 \\[1 em] \color{blue}{ x = 0} ~~ \text{or} ~~ 6x^2-25x+2 & = 0 \end{aligned} $$One solution is $ \color{blue}{ x = 0 } $. Use second equation to find the remaining roots.
Step 2:
The solutions of $ 6x^2-25x+2 = 0 $ are: $ x = \dfrac{ 25 }{ 12 }-\dfrac{\sqrt{ 577 }}{ 12 } ~ \text{and} ~ x = \dfrac{ 25 }{ 12 }+\dfrac{\sqrt{ 577 }}{ 12 }$.
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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