Answer: You didn't say how long you've had your dracaena or what the weather conditions were when you got it. This information can help us solve the problem. But, based upon the information you did share, I will do my best to help you help your plant. As a rule, dracaena makes an easy care houseplant. They will grow in low to moderate light and prefer fast draining soils that are allowed to dry out slightly between waterings. If your plant came from a greenhouse where growing conditions were perfect, it's probably having a hard time adjusting to the conditions in your home. And, if it was subjected to cold air or bright sunlight on its journey to your home, it could be showing signs of distress from these, as well.
So, here's my suggestion. Prune off any dead plant parts. If the roots are healthy a new stem (or two) will develop. Place the plant in a site where it gets low to moderate light - somewhere out of drafts from open doors or windows and away from heater/air conditioner ducts. Allow the soil to dry out slightly between waterings. The top of the soil should be dry and barely pulling away from the sides of the pot between waterings. Use bottled water when you do water (browing leaf tips can indicate dry indoor air or too many minerals in the water), and water thoroughly so water freely flows from the drainage holes.
I hope these suggestions helps you help your plant regain its health!
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