The parabolas defined by the equations y = x^2 + 4x + 6 and y = 2x^2 + 7x - 4 intersect at points and (a,b) and (c,d), where c >= a. What is c-a?
Set the equations equal
2x^2 + 7x - 4 = x^2 + 4x + 6 subtract the right side from the left
x^2 + 3x - 10 = 0 factor as
(x + 5) ( x - 2) = 0
Set each factor to 0 and solve for x
x + 5 = 0 x - 2 = 0
x = -5 = a x = 2 = c
So
c - a = 2 - (-5) = 7
