Transportation of minerals across root hair occurs due to
Passive absorption
Active absorption
Minerals are absorbed actively by roots since the concentration is higher in the root cells than in the soil. Nutrients are absorbed actively by the root cells with the utilisation of ATP. As a result, the concentration of ions in the xylem vessels is more in comparison to the soil water.
Mostly the movement of mineral ions into root occurs due to diffusion. Diffusion is a passive movement across a potential gradient.