Find the zeroes of the quadratic polynomial $4s^{2}-4s+1$ and verify the relationship between the zeroes and the coefficients.

(N/A) Given polynomial: $p(s) = 4s^{2}-4s+1$.
To find the zeroes,set $p(s) = 0$:
$4s^{2}-4s+1 = 0$
$(2s-1)^{2} = 0$
$2s-1 = 0 \implies s = \frac{1}{2}$.
Thus,the zeroes are $\frac{1}{2}$ and $\frac{1}{2}$.
Verification:
Sum of zeroes $= \frac{1}{2} + \frac{1}{2} = 1 = \frac{-(-4)}{4} = \frac{-(\text{Coefficient of } s)}{\text{Coefficient of } s^{2}}$.
Product of zeroes $= \frac{1}{2} \times \frac{1}{2} = \frac{1}{4} = \frac{\text{Constant term}}{\text{Coefficient of } s^{2}}$.
Hence,the relationship is verified.