No, Roundup (glyphosate) will not kill a tree from soil runoff or root absorption when used as directed for lawn weeds.
Trees are only harmed if spray directly contacts:
The flowers at the tree base surviving proves the herbicide didn't move through soil. Tree decline likely has another cause (drought, disease, construction damage, etc.).
Black Sooty Bark on Flowering Peach: Scale Insects and Horticultural Oil Fix
Saving Mature Catalpa from Borers, Drought, and Age
Indoor Pine White Sticky Substance: Honeydew from Insects
Borers in Mature Maple Trees: Identification and Treatment Options
Killing a Tree with Herbicide: Cut-Stump vs. Frill Methods
Killing a Large Tree Damaging a Deck and Pipes: Cut-Stump Method
Red Acer (Maple) Larvae Infestation: Atomic Grow Foliar Cleanup and Systemic Healing
Indoor Lime Tree Scale & Pollination: Bath, Oil, and Bees
Apple Tree Bark Shedding: Normal Spring Process
Apple Tree Bark Peeling: Normal Aging or Pest Problem?
Eradicating Yucca Without Salt: Herbicide on Cut Stems or Light Exclusion
Cherry Tree Damaged by Late Dormant Spray: Will It Recover?
Removing Grass from Unmortared Brick Patio: Ecological vs. Chemical
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