Roots of Quadratics and Their Relationship

Consider the quadratic equation given by:

$$ x^2 - (2k + 1)x + k^2 - k = 0 $$

where $k$ is a constant. We want to analyze the relationships between two quantities.

Quantity A: The number of distinct real roots of the equation for a specific value of $k$.

Quantity B: The value of $k$ when the quadratic equation has exactly one real root.

Determine the relationship between Quantity A and Quantity B.