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avatar+2765 

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.

tertre  Mar 12, 2017
 #1
avatar+12565 
0

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

ElectricPavlov  Mar 12, 2017
 #2
avatar+2765 
0

Thanks guys!

tertre  Mar 12, 2017
 #3
avatar+87334 
+5

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

 

 

cool cool cool

CPhill  Mar 12, 2017

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