Question
Find roots of polynomial $$ p(x) = a^2-a^3 $$
Answer
The roots of polynomial $ p(a) $ are:
$$ \begin{aligned}a_1 &= 0\\[1 em]a_2 &= 1 \end{aligned} $$Explanation
Step 1:
Write polynomial in descending order
$$ \begin{aligned} a^2-a^3 & = 0\\[1 em] -a^3+a^2 & = 0 \end{aligned} $$Step 2:
Factor out $ \color{blue}{ -a^2 }$ from $ -a^3+a^2 $ and solve two separate equations:
$$ \begin{aligned} -a^3+a^2 & = 0\\[1 em] \color{blue}{ -a^2 }\cdot ( a-1 ) & = 0 \\[1 em] \color{blue}{ -a^2 = 0} ~~ \text{or} ~~ a-1 & = 0 \end{aligned} $$One solution is $ \color{blue}{ a = 0 } $. Use second equation to find the remaining roots.
Step 3:
To find the last zero, solve equation $ a-1 = 0 $
$$ \begin{aligned} a-1 & = 0 \\[1 em] a & = 1 \end{aligned} $$This page was created using
Polynomial Roots Calculator