Answer: You can try pulling or digging these out, but it will be a big job to get the whole root. If you leave the root behind it will come right back.
You can try hoeing off the weeds just below the ground level, this would kill off most annual weeds if you catch them early in the season and will help weaken perennial weeds. A swivel or stirrup hoe that you pull back and forth is great for this.
Once you have cut them down, you can try to smother them with a few layers of damp newspaper (overlap the edges to exclude light) topped with several inches of organic mulch. This should prevent most weeds from coming up. The paper will eventually rot down and add to the organic matter in the soil.
Those weeds that do manage to push their way through that can be spot treated with an herbicide containing glyphosate. In a flower bed situation you may find that the wipe on application method is better than the spray -- because the spray will kill desirable plants in addition to weeds.
You may have to try handing weeding close to your plants and then mulch in between them. The first year or two are the worst for weeds in a new flower bed. Once you control them it gets better over time as long as you never allow the weeds to flower and set seed. Keep an eye out during the fall because that is when many weeds germinate and begin growing.
In the meantime, keep your mulch fluffed and topped up to help prevent new weeds from germinating. As your perennials grow and fill in the space they will also help to shade out the weeds. Good luck with your flower garden!
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