Find the zeroes of the following quadratic polynomial and verify the relationship between the zeroes and the coefficients: $4u^{2} + 8u$.

(N/A) Given polynomial: $p(u) = 4u^{2} + 8u$.
To find the zeroes,set $p(u) = 0$:
$4u^{2} + 8u = 0$
$4u(u + 2) = 0$
This implies $4u = 0$ or $u + 2 = 0$.
So,$u = 0$ or $u = -2$.
The zeroes are $0$ and $-2$.
Verification:
Comparing $4u^{2} + 8u$ with $au^{2} + bu + c$,we get $a = 4, b = 8, c = 0$.
Sum of zeroes $= 0 + (-2) = -2$.
Relationship: $\frac{-b}{a} = \frac{-8}{4} = -2$.
Since Sum of zeroes $= \frac{-b}{a}$,the relationship is verified.
Product of zeroes $= 0 \times (-2) = 0$.
Relationship: $\frac{c}{a} = \frac{0}{4} = 0$.
Since Product of zeroes $= \frac{c}{a}$,the relationship is verified.