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.
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 !