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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?

 Feb 4, 2022
 #1
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c - a = 22.

 Feb 4, 2022
 #2
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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.   

 Feb 4, 2022

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