Let $\displaystyle f$ be a quadratic polynomial function of $\displaystyle z $ with two different roots $\displaystyle z_1$ and $\displaystyle z_2$. Given that a branch of $\displaystyle z$ of the square root of $\displaystyle f$ exists in a domain $\displaystyle D$, demonstrate that neither $\displaystyle z_1$ nor $\displaystyle z_2$ can belong to $\displaystyle D$. If $\displaystyle D$ had a double root, would the analogous statement be true?