Find roots of polynomial $$ p(x) = 36w-w^2 $$

The roots of polynomial $ p(w) $ are:

$$ \begin{aligned}w_1 &= 0\\[1 em]w_2 &= 36 \end{aligned} $$

Step 1:

Write polynomial in descending order

$$ \begin{aligned} 36w-w^2 & = 0\\[1 em] -w^2+36w & = 0 \end{aligned} $$

Step 2:

Factor out $ \color{blue}{ -w }$ from $ -w^2+36w $ and solve two separate equations:

$$ \begin{aligned} -w^2+36w & = 0\\[1 em] \color{blue}{ -w }\cdot ( w-36 ) & = 0 \\[1 em] \color{blue}{ -w = 0} ~~ \text{or} ~~ w-36 & = 0 \end{aligned} $$

One solution is $ \color{blue}{ w = 0 } $. Use second equation to find the remaining roots.

Step 3:

To find the second zero, solve equation $ w-36 = 0 $

$$ \begin{aligned} w-36 & = 0 \\[1 em] w & = 36 \end{aligned} $$

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