Four times a number less than the square of the same number is at most 5. What are the possible integral values of the number?

Question

Four times a number less than the square of the same number is at most 5. What are the possible integral values of the number?

Answer 1

N^2 -4N < 5

N^2 -4N -5 < 0

(N-5)(N+1) < 0

N-5 < 0 and N+1 > 0 or N-5 > 0 and N+1 < 0

the factors have to be of opposite signs for their product to be non-positive

Either N < 5 and N > -1 which means N= -1, 0, 1, 2, 3, 4, or 5

or N>5 and N<-1 which is impossible

so, N = either -1, 0, 1, 2, 3, 4, or 5