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?
x^2 + 4x + 6 = 2x^2 + 7x - 4 rearrange as
x^2 + 3x - 10 = 0 factor
(x - 2) ( x + 5) = 0 set each factor to 0 and solve for x and we have that
x = 2 and x = -5
So
c = 2 and a = -5
And
c - a = 2 - (-5) = 2 + 5 = 7
