For each of the following,find a quadratic polynomial whose sum and product of the zeroes are $\frac{21}{8}$ and $\frac{5}{16}$ respectively. Also,find the zeroes of these polynomials by factorisation.

(A) Given that,the sum of zeroes $S = \frac{21}{8}$ and the product of zeroes $P = \frac{5}{16}$.
The required quadratic polynomial is given by $f(x) = k(x^2 - Sx + P)$,where $k$ is a constant. Taking $k = 16$ to clear the denominators:
$f(x) = 16(x^2 - \frac{21}{8}x + \frac{5}{16}) = 16x^2 - 42x + 5$.
To find the zeroes,set $f(x) = 0$:
$16x^2 - 42x + 5 = 0$.
Splitting the middle term: $16x^2 - 40x - 2x + 5 = 0$.
$8x(2x - 5) - 1(2x - 5) = 0$.
$(8x - 1)(2x - 5) = 0$.
Thus,the zeroes are $x = \frac{1}{8}$ and $x = \frac{5}{2}$.