The roots of the quadratic equation x²-7x+c = 0
differ by 1. Find c
let r = one root and r-1 be the other root.
Substitute r for x:
Eq. 1: r²-7r+c = 0
Substitute (r-1) for x
Eq. 2: (r-1)²-7(r-1)+c = 0
Simplify Eq. 2:
(r-1)(r-1)-7r+7+c = 0
r²-2r+1-7r+7+c = 0
r²-9r+8+c = 0
So we have this system of equations:
Get the 8 off the right side of the second equation by
adding -8 to both sides
Multiply the second equation by -1 and add the two equations term by term:
r²-7r+c = 0
-r²+9r-c = 8
------------
2r = 8
r =
r = 4
Substitute that in
r²-7r+c = 0
Edwin