If something is ineradicable, you cannot take it out or wipe it away — it stays. The picture behind the word is a plant whose roots you cannot dig up.

if something如果有樣東西 is ineradicable是無法根除的 you cannot你就沒辦法 take it out把它拿掉 or或 wipe it away抹去它 it它 stays會一直留著 the picture behind the word這個詞背後的畫面 is是 a plant一株植物 you cannot dig up你挖不出 whose roots它的根

People use it for habits, fears, beliefs, and problems that will not go, even when you try hard.

people use it for人們會用它來形容 that will not go那些怎麼樣都去不掉的 habits, fears, beliefs, and problems習慣、恐懼、信念和問題 even when you try hard即使你很努力嘗試

It is a formal, bookish word; in daily talk you would more often say you cannot get rid of it, or it will not go away.

it is a formal, bookish word它是個正式、書面的詞 in daily talk日常說話裡 you would more often say你比較常會說 you cannot get rid of it你擺脫不了它 or或 it will not go away它不會消失

Though actually, writers sometimes use it a little loosely for anything very hard to change, not only things that are truly impossible to remove. You will see it in serious writing about prejudice, disease, a deep habit, or a stain on someone's name.

though actually不過其實 writers sometimes use it a little loosely作家有時候會用得比較鬆 for anything very hard to change指任何很難改變的東西 not only things that are truly impossible to remove不只是真的除不掉的東西 you will see it你會看到它出現 in serious writing在嚴肅的文章裡 about prejudice, disease, a deep habit, or a stain on someone's name談偏見、疾病、根深蒂固的習慣，或某人名聲上的污點