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The parabolas defined by the equations y = -x^2 - x + 1 and y = 2x^2 - 3x intersect at points (a,b) and (c,d), where c >= a. What is c - a? Express your answer as a common fraction.

 Jun 14, 2021
 #1
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Set  the equations     =

 

-x^2   -x  +  1  =   2x^2   -3x        rearrange as

 

3x^2  - 2x  -  1     =   0              factor  as

 

(3x  + 1)  ( x - 1)    =   0

 

Setting both factors to 0  and solving  for  x  produces

 

 x =  a =  -1/3           x  =   c   =  1

 

So

 

c   -  a    =

 

1 - ( -1/3)   =

 

4 / 3

 

 

cool cool cool

 Jun 14, 2021

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