The centre of mass of a body is located at the origin. The x...

The $x$-coordinate of the centre of mass is given by $X_{cm} = \dfrac{\sum m_i x_i}{\sum m_i}$.

Given $X_{cm} = 0$, we have $\sum m_i x_i = 0$.

Since the mass of each particle is positive ($m_i > 0$), the sum $\sum m_i x_i = 0$ is possible only in two cases.

First, $x_i = 0$ for all particles. In this case, all $x$-coordinates are zero, which means they are entirely non-negative.

Second, some $x_i > 0$ and some $x_i < 0$. In this case, the $x$-coordinates are positive for some particles and negative for others.

The $x$-coordinates cannot be entirely positive or entirely negative, as that would result in a non-zero centre of mass.

Answer: could be entirely non-negative; could be positive for some particles and negative for others