The parabolas defined by the equations y = -x^2 - x + 1 and y = x^2 - 3x - 3 intersect at points (a,b) and (c,d), where c >= a. What is c - a? Express your answer as a common fraction.
-x^2 - x + 1 = x^2 - 3x - 3 rearrange as
2x^2 - 2x - 4 = 0 divide through by 2
x^2 - x - 2 = 0 factor as
( x - 2) ( x + 1) = 0
Set each factor to 0 and solve for x and we get that
x = 2 = c and x = -1 = a
c - a =
2 - (-1) =
3
