In my Chinese textbook, 谦虚好学 is used, and 虚心求教 is used as well. They both mean modest, so when should I use each one?
謙虛好學 means be modest and loves learning. 虛心求教 means be modest and appeals others to teach. To verified this you can search 謙虛 in dictionary owned by Ministry of education in Taiwan. It shows the description 虛心謙讓不自滿。(modest). In the dictionary 好學 described as 喜歡學習。(love learning). In the dictionary 虛心 described as 謙退容物，心不自滿。(modest). In the dictionary 求教 described as 懇請他人指教。(appeal others to teach).
Use quotation marks you can find tons of example on google for example: "謙虛好學" and "虛心求教" google search engine do show you that how much data it found. If there are so many people use this way it is more reliable. You can determine the reliability of usages.
From some www.newxue.com:
I won't be able to translate them all.
"虚心" shows that one is will to learn from others, as in "虚心学习", "虚心听取别人的意见".
"谦虚" is used in as sense that one feels/says that he might not meet how others say, like 小明谦虚地说：“你们别夸我了，我做得还很差。”
"谦虚" can also be used as verb, which mean one says something in a "谦虚" way. "虚心" does not have this usage.
Feel free to modify to improve this post. I feel my English is a little limited to explain this.
謙虛好學 means "modest and eager to learn", usually used by teachers to praise the students. When you use it on yourself, praising yourself as "好學", you are not "謙虛" anymore.
虛心求教 means "seeking help/solution/knowledge in a modest manner/attitude"; in addition, "虛心" also implies that you are ready to un-learn some of your prior knowledge. You can use it on yourself but you must be very careful.
My two cents. In the word 谦虚好学, 谦虚 can be replaced by 虚心 and change to 虚心好学. Both 谦虚好学 and 虚心好学 are accepted words with the same meaning. However, in the word 虚心求教, 虚心 can not be replaced by 谦虚. It does not sound right. I think, although both 谦虚 and 虚心 have the meaning of being modest, 谦虚 has an extra layer of humility, being humble, a trait ascribed to successful people.
You may see
虚心求教 are having the same meaning, but in fact it is not.
虚心 both means modest but the usage is slightly different.
谦虚: When people are giving you a compliment / asking you for advice, you are showing a quality self-cultivation which do not behave arrogant, sees other as equal.
虚心: When you are asking other people for advice, example like your teacher / your elders (people who are having more experience than you), you are behaving like you know everything. Instead, you are showing a quality attitude like a cup of water which is never full (The cup represent you, and the water represent your knowledge to certain thing), because learning anything should always behave like there are a lot to learn, do not be smart.
谦虚好学: While other people sees you as a veteren, you do not arrogant. Instead, you also behave like newbie, there are a lot to learn. Thus,
好学 means never stop learning
虚心求教: While learning from veteren, you do not be smart. Instead, you are behaving good quality of attitude, respecting elders while learning from them. Thus
求教 is begging for knowledge