Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients

$4 x^{2}-4 x+1=0$

$\Rightarrow(2 x)^{2}-2(2 x)(1)+(1)^{2}=0$

$\Rightarrow(2 x-1)^{2}=0 \quad\left[\because a^{2}-2 a b+b^{2}=(a-b)^{2}\right]$

$\Rightarrow(2 x-1)^{2}=0$

$\Rightarrow x=\frac{1}{2}$ or $x=\frac{1}{2}$

Sum of zeroes $=\frac{1}{2}+\frac{1}{2}=1=\frac{1}{1}=\frac{-(\text { coefficient of } x)}{\text { coefficient of } x^{2}}$

Product of zeroes $=\frac{1}{2} \times \frac{1}{2}=\frac{1}{4}=\frac{\text { constant term }}{\text { coefficient of } x^{2}}$