+1501 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.)
+1950 In order to find all of ordered pairs that work, we just have to write an equation.
If the two graphs intersect, then we have x3+x2−3x+5=x3+2x2.
Combing all like terms and moving all terms to one side, we get x2+3x−5=0.
Using the quadratic equation, we get
x=√29−32≈1.193x=−√29−32≈−4.193
Plugging these two values back into our equations from earlier, we get
y≈4.541y≈−38.541
So our two orders pairs approximately are
(1.193,4.541),(−4.193,−38.541)
Thanks! :)
