To placate someone is to do or say something that makes them stop being angry or upset with you. It is not the same as solving the problem — that is the whole flavour of the word. You placate a person by giving them something, apologising, agreeing with part of what they say, or making a small change, so that they calm down. Whether the thing they were angry about actually got fixed is a separate question, and often it did not. Because of this, `placate` carries a faint smell of managing people. When a newspaper says the government made a change 'to placate angry farmers', the writer is usually hinting that the change was small and the real purpose was to quiet the noise. When you say a mother placated her crying child with a biscuit, you are not criticising her — the child was upset, the biscuit worked. So the word is not always negative, but it always looks at the calming-down from the outside, as an action one person performs on another. It is a fairly formal, written word. In speech a Taiwanese student is far more likely to hear 'calm someone down' or 'keep someone happy'. You placate a person (or a group, or in older religious writing, an angry god) — the object is the angry one, never the anger itself, so 'placate his anger' sounds wrong to a native ear even though it looks logical.