If the zeroes of the polynomial $x^2+px+q$ are in the ratio $2:3$, then prove $6p^2=25q.$

Find a quadratic polynomial whose sum and product respectively of the zeroes are given. Also find the zeroes of the polynomial.

$\frac{-8}{3}, \frac{4}{3}$

Find a quadratic polynomial whose sum and product respectively of the zeroes are given. Also find the zeroes of the polynomial.

$0, \frac{-3}{5}$