You Asked for an evicence for violence and hatred in Quran..in fact there are many!! Here is an example:
"[4.89] They desire that you should disbelieve as they have disbelieved, so that you might be (all) alike; therefore take not from among them friends until they fly (their homes) in Allah's way; but if they turn back, then seize them and kill them wherever you find them, and take not from among them a friend or a helper."
"[4.91] ... therefore if they do not withdraw from you, and (do not) offer you peace and restrain their hands, then seize them and kill them wherever you find them; and against these We have given.you a clear authority."
