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What are the coordinates of the points where the graphs of f(x) = x^3 - x^2 + x + 1 and g(x) = x^3 + x^2 + x + 1 intersect? Give your answer as a list of points separated by semicolons, with the points ordered such that their x-coordinates are in increasing order. (So "(1,-3); (2,3); (5,-7)" - without the quotes - is a valid answer format.)

 Apr 9, 2021
 #1
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Set  the equations  equal

 

x^3  - x^2  + x + 1  =  x^3 + x^2 + x + 1

 

Subtracting out common terms  we  get

 

-x^2   =  x^2          rearrange  as

 

x^2  + x^2   =  0

 

2x^2  =  0

 

x^2  =  0

 

x =  0

 

And putting  this value  into either equation  we get  that  y  =  1

 

So.....intersection pt =  (0, 1)

 

 

cool cool cool

 Apr 9, 2021

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