Question

x^3+x^2+x-p=0. p is a prime number that i need to find so that the equation has at least one rational root.

Answer 1

i know that p=3 and x=1 but i don't know how to get the answer.

Answer 2

@Mertsj

Answer 3

@jim_thompson5910 @wio

Answer 4

yup i got it

Answer 5

K no problem. @abc123!

Answer 6

thanks

Answer 7

If p is a prime number, then that means that the only divisor of p are -p, p, 1, -1. By the rational roots theorem, the possible roots of the polynomial are: -p, p, 1, -1. We notice that when we put 1 in place of x and simplify, we get 3 - p = 0. This suggests that if p = 3 ( a prime number), then the equation would have at least one rational zero which would be at x = 1. Hence, p = 3, gives the cubic function at least one rational root at x = 1. Do you understand?