In the long run, for the children to trust their parents, the parents must first win the confidence of the children. One of the important steps in that is to have all the answers for their children's questions. There will be tough questions, embarrassing questions, questions in areas that we are not exposed to, new progresses in science, economics, geography, civics, etc.
Irrespective of our knowledge in the area, we should have an answer that will continue to keep the bond with children. If we are not familiar with the area, we can always look it up in the world wide web and respond to the children. If it is embarrassing questions we should have the clear thinking on whether it is time for the child to learn the truth behind certain areas - is he/she of appropriate age to start learning these things.
A sure way of losing children's confidence is dismissing their questions with any kinds of answers like "Don't ask me all this, ask your teacher", "I don't know these things", "Ask Maths to your mother" or "Ask Science to your father", etc. Since the parents are the main support for the children long into the future, it is important that they be seen as role models.
For that, build confidence by giving as many answers as possible and keep the candle of creativity in the child burning bright. And for the rest "Please wait, while I look it up in the internet, so that I can also learn" would be a good way of reinforcing the feeling that they can come to the parents for any items / issues.