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?
c - a = 22.
Equate the two:
x^2 + 4x + 6 = 2x^2 + 7x - 4
Simplify:
x^2 + 3x -10 = 0
Factor:
(x-2)(x+5) = 0
So the two roots (x-values) are: x = 2 and x = -5. These are c and a, respectively.
