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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?

 Dec 22, 2020
 #1
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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

 

 

cool cool cool

 Dec 22, 2020

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