This question is really just theoretical. "Which of the following values are <em>possible</em> rational roots for this plant" It wants you to apply the rational root theorem in the form of s/t, not actually solve it. I think the answer is everything but zero when you apply the rational root theorem.
I'm still not 100% sure of this, I was trying to find the answer myself but now that I've brought up the rational root theorem maybe someone could provide a better answer.
0 isn't one of them. There are 5 altogether. That comes from 7x^5. The 5 determines how many roots will solve the polynomial.
1 won't work either. Nor will minus 1. Both leave remainders. The only way to get started is to do this by brute force. Go down the list and see who gives a zero.
According to this graph, none of them work. There is one solution and it is marked on the graph. The 1 solution is just larger than -1. Check the question again and if it is different, put a comment at the bottom.