Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively.

$\sqrt{2}, \dfrac{1}{3}$

For given roots,

Quadratic equation : x² - (Sum of roots)x + (Product of roots) = 0

Substituting values we get :

$\Rightarrow x^2 - \sqrt{2}x + \dfrac{1}{3} = 0 \\[1em] \Rightarrow \dfrac{3x^2 - 3\sqrt{2}x + 1}{3} = 0 \\[1em] \Rightarrow 3x^2 - 3\sqrt{2}x + 1 = 0.$

Hence, required quadratic equation is $3x^2 - 3\sqrt{2}x + 1 = 0$.