The difference of the two solutions of x^2−17x+c=0 is 1. find the solutions.

Hmm,
we see that the middle term is negative
that tells us that the factors must also be negative because if they were different signs then they would have to be 0,1, or -1,0 which wouldn't work because x doesn't factor out, well, if c=0, then it would get x=17 and 0 which doesn't work

well

what 2 numbers are 1 apart, and are negative and add to -17
-8 and -9
multily them
72

c=72
x^2-17x+72=0
if we factord
(x-8)(x-9)=0
theh zeroes are x=8 and 9