Question
Find roots of polynomial $$ p(x) = s^3+12s^2+20s $$
Answer
The roots of polynomial $ p(s) $ are:
$$ \begin{aligned}s_1 &= 0\\[1 em]s_2 &= -2\\[1 em]s_3 &= -10 \end{aligned} $$Explanation
Step 1:
Factor out $ \color{blue}{ s }$ from $ s^3+12s^2+20s $ and solve two separate equations:
$$ \begin{aligned} s^3+12s^2+20s & = 0\\[1 em] \color{blue}{ s }\cdot ( s^2+12s+20 ) & = 0 \\[1 em] \color{blue}{ s = 0} ~~ \text{or} ~~ s^2+12s+20 & = 0 \end{aligned} $$One solution is $ \color{blue}{ s = 0 } $. Use second equation to find the remaining roots.
Step 2:
The solutions of $ s^2+12s+20 = 0 $ are: $ s = -10 ~ \text{and} ~ s = -2$.
You can use step-by-step quadratic equation solver to see a detailed explanation on how to solve this quadratic equation.
This page was created using
Polynomial Roots Calculator