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

 Apr 12, 2021
 #1
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Where they intersect they are equal

 

-x^2 -x +1       =       2x^2 -1       gather 'like' terms and simplify

3x^2 +x -2 = 0          Use Quadratic Formula to find    x = 2/3  and -1        these are   c   and   a    in your question

 

Take it from here !  

 Apr 12, 2021
edited by ElectricPavlov  Apr 12, 2021

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