Question
Find roots of polynomial $$ p(x) = d^3-4d^2+5d $$
Answer
The roots of polynomial $ p(d) $ are:
$$ \begin{aligned}d_1 &= 0\\[1 em]d_2 &= 2+i\\[1 em]d_3 &= 2-i \end{aligned} $$Explanation
Step 1:
Factor out $ \color{blue}{ d }$ from $ d^3-4d^2+5d $ and solve two separate equations:
$$ \begin{aligned} d^3-4d^2+5d & = 0\\[1 em] \color{blue}{ d }\cdot ( d^2-4d+5 ) & = 0 \\[1 em] \color{blue}{ d = 0} ~~ \text{or} ~~ d^2-4d+5 & = 0 \end{aligned} $$One solution is $ \color{blue}{ d = 0 } $. Use second equation to find the remaining roots.
Step 2:
The solutions of $ d^2-4d+5 = 0 $ are: $ d = 2+i ~ \text{and} ~ d = 2-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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