Find the zeroes of the following polynomial by the factorisation method and verify the relationship between the zeroes and the coefficients of the polynomial:
$2s^{2} - (1 + 2\sqrt{2})s + \sqrt{2}$

(N/A) Let $f(s) = 2s^{2} - (1 + 2\sqrt{2})s + \sqrt{2}$.
$= 2s^{2} - s - 2\sqrt{2}s + \sqrt{2}$
$= s(2s - 1) - \sqrt{2}(2s - 1)$
$= (2s - 1)(s - \sqrt{2})$
The value of $f(s)$ is zero when $2s - 1 = 0$ or $s - \sqrt{2} = 0$.
Thus,$s = \frac{1}{2}$ or $s = \sqrt{2}$.
So,the zeroes of the polynomial are $\frac{1}{2}$ and $\sqrt{2}$.
Verification:
Sum of zeroes $= \frac{1}{2} + \sqrt{2} = \frac{1 + 2\sqrt{2}}{2} = \frac{-[-(1 + 2\sqrt{2})]}{2} = \frac{-(\text{Coefficient of } s)}{\text{Coefficient of } s^{2}}$.
Product of zeroes $= \frac{1}{2} \times \sqrt{2} = \frac{\sqrt{2}}{2} = \frac{1}{\sqrt{2}} = \frac{\text{Constant term}}{\text{Coefficient of } s^{2}}$.
Hence,the relationship between the zeroes and the coefficients is verified.