Why is my Cordyline dying?
Your cordyline and palm are dying because you transplanted them in the middle of the growing season and have damaged the fiberous root system. If you wanted to move them you should have waited until the dormant season in the middle of the winter. Those straggly bits of root are extremely important. If the leaves of the palms are going brown then I think it may be too late for them. About the only thing that may help is too cut back dead or damaged growth and heavily water them on a regular basis, as the plants are going into shock and dropping foliage to reduce evapotranspiration, they need as much water as possible (Arid Plants or Not!) . You could also try using a liquid sea weed feed this is proven to promote foliage. All the best.
