The parabolas defined by the equations y=-x^2-x+1 and y=2x^2-7 intersect at points (a,b) and (c,d), where c\ge a. What is c-a?
Set the equations equal
2x^2 - 7 = -x^2 - x + 1 simplify
3x^2 + x - 8 = 0
Using the quadratic formula
x = -1 ±√ [1^2 - 4 (3) (-8) ] -1 ±√ 97
____________________ = ________
2 * 3 6
c - a = 2√97 / 6 = √97 / 3
