+0

# Mathquestion3

0
75
3
+1166

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
Sort:

#1
+10614
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
+1166
0

Thanks guys!

tertre  Mar 12, 2017
#3
+76929
+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

CPhill  Mar 12, 2017

### 23 Online Users

We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details