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

4s² - 4s + 1

Let,

⇒ 4s² - 4s + 1 = 0

⇒ 4s² - 2s - 2s + 1 = 0

⇒ 2s(2s - 1) - 1(2s - 1) = 0

⇒ (2s - 1)(2s - 1) = 0

⇒ (2s - 1)= 0 or (2s - 1) = 0

⇒ 2s = 1 or 2s = 1

⇒ s = $\dfrac{1}{2}$ or s = $\dfrac{1}{2}$.

Sum of the zeroes = $\dfrac{1}{2} + \dfrac{1}{2} = 1 = \dfrac{-(-4)}{4} = \dfrac{-\text{(Coefficient of s)}}{\text{(Coefficient of s}^2)}$.

Product of zeroes = $\dfrac{1}{2} \times \dfrac{1}{2} = \dfrac{1}{4} = \dfrac{\text{Constant term}}{\text{Coefficient of s}^2}$

Hence, for zero of the polynomial 4g² - 4g + 1, g = $\dfrac{1}{2}, \dfrac{1}{2}$.