Yes, they do. Plants seek out nutrients through their roots. We can conduct experiments to observe this.
On a loose and infertile piece of land, create a circle with a diameter of half a meter. Plant some seeds of crops within this circle and bury a lump of stable manure in the center at a depth of 20-25 centimeters. Do not apply any additional fertilizer elsewhere in the circle and remove all weeds from it. Allow the plants to grow vigorously. When the crops have grown significantly, carefully dig up the soil within the circle. You will observe that all the plants have extended their roots towards the central manure, tightly wrapping their roots around it, as if they are gathering for a feast.
We can also conduct a small-scale experiment indoors. Prepare a cup of ordinary gelatin solution using warm water (mixing a few gelatin sheets in a cup of water), then pour it into a plate and allow it to solidify. Plant a few germinated seeds along the edges of this gelatin and press them into the gelatin. Place a small piece of potassium nitrate or another type of fertilizer in the center of the gelatin. After three to four days, you will clearly see that all the roots have grown towards the center and wrapped around the piece of fertilizer.
In reality, the growth of plant roots is always in search of “food.” Plant roots always extend towards areas where the concentration of nutrients in the soil solution is higher.