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

$-\dfrac{1}{4}, \dfrac{1}{4}$

For given roots,

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

Substituting values we get :

$\Rightarrow x^2 - \Big(-\dfrac{1}{4}\Big)x + \Big(\dfrac{1}{4}\Big) = 0 \\[1em] \Rightarrow x^2 + \dfrac{x}{4} + \dfrac{1}{4} = 0 \\[1em] \Rightarrow \dfrac{4x^2 + x + 1}{4} = 0 \\[1em] \Rightarrow 4x^2 + x + 1 = 0.$

Hence, required quadratic equation is 4x² + x + 1 = 0.