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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.)

 Apr 2, 2024
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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?

 

Hello ABJelly!

 

\(x^3 + x^2 - 3x + 5 = x^3 + 2x^2\\ x^2+3x-5=0\\ x_{f,g}=-1.5\pm\sqrt{2.25+5}\\ x_{f,g}=\frac{1}{2}(3\pm\sqrt{29})\\ x_{f,g}\in \{ -4.19258,\ 1.19258\}\)

\(y_g\in \{-38.540659,4.540659\}\\ \color{blue}So\ ( -4.19258,-38.540659),(1.19258,4.540659)\)

 

laugh !

 Apr 2, 2024
edited by asinus  Apr 2, 2024

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