SOLUTION: The curves y = 2x^3 and y = (2-x)(5x+6) intersect in 3 points. Find the x-coordinates of these points.

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Question 1183633: The curves y = 2x^3 and y = (2-x)(5x+6) intersect in 3 points. Find the x-coordinates of these points.
Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


No; they do not intersect in three points....

2x%5E3=%282-x%29%285x%2B6%29
2x%5E3%2B5x%5E2-4x-12=0

The rational roots theorem and synthetic division then show

2x%5E3%2B5x%5E2-4x-12=%282x-3%29%28x%2B2%29%5E2

The graphs intersect at TWO points, with x coordinates -2 and 3/2.