+4622 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.
+37153 Setting the euations equal to each other and using the Quadratic formula to solve results in
x = 4/6 and -1 and substituting these valuse of x results in y = -.1111 and 1 respectively
a,b c, d = -1,1 and 4/6, -.11111
Then c- a = 4/6 - (-1) = 10/6
+129899 Set these equal
-x^2 - x + 1 = 2x^2 - 1 simplify
0 = 3x^2 + x - 2 factor
0 = (3x - 2) ( x + 1) set both factors = 0 and the x intersection points are x = 2/3 and x = -1
So...we have the intersection points are (a,b) and (c,d) = (-1,b) and (2/3, d)
So.....c - a = 2/3 - (-1) = 1 + 2/3 = 5/3
