The first plant the princess examines has a label of 0=7x5+3x3-2x+1.

She digs up the roots of several plants. Which of the following values are possible rational roots for this plant?

There may be more than one correct answer. Select all correct answers.

17

7

-17

-7

0

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.

1/7, 7, - 1/7, - 7

Step-by-step explanation:

This question is really just theoretical. "Which of the following values are possible 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.