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What are the coordinates of the points where the graphs  of f(x)=x^3 + x^2 - 3x + 5 and g(x) = x^3 + 2x^2 intersect?  

 

Give your answer as a list of points separated by commas, with the points ordered such that their -coordinates are in increasing order. (So "(1,-3), (2,3), (5,-7)" - without the quotes - is a valid answer format.)

 Jan 23, 2025
 #1
avatar+130317 
+1

x^3 + x^2 -3x + 5 =  x^3 + 2x^2

 

2x^2 + 3x - 5  = 0

 

(2x + 5) ( x -1) = 0

 

2x + 5  = 0                                                   x - 1 =  0

 

x = -5/2                                                           x = 1

 

y = (-5/2)^3 + 2(-5/2)^2 = -25/8                y  = (1)^3  + 2(1)^2  =  3

 

(-5/2, -25/8) ,  ( 1, 3)

 

cool cool cool

 Jan 23, 2025

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