Find roots of polynomial $$ p(x) = 4u^2+8u $$

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

$$ \begin{aligned}u_1 &= 0\\[1 em]u_2 &= -2 \end{aligned} $$

Step 1:

Factor out $ \color{blue}{ 4u }$ from $ 4u^2+8u $ and solve two separate equations:

$$ \begin{aligned} 4u^2+8u & = 0\\[1 em] \color{blue}{ 4u }\cdot ( u+2 ) & = 0 \\[1 em] \color{blue}{ 4u = 0} ~~ \text{or} ~~ u+2 & = 0 \end{aligned} $$

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

Step 2:

To find the second zero, solve equation $ u+2 = 0 $

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

Polynomial Roots Calculator