In a reference (O, i, j), the points A (-12, 1150) and B (10, -500). The function f is defined on (-20, 10) by: f(x) = x^ 4 +2.25 x^3-44.5x^2-260x+100

Question

In a reference (O, i, j), the points A (-12, 1150) and B (10, -500). The function f is defined on (-20, 10) by:  f(x) = x^ 4 +2.25 x^3-44.5x^2-260x+100
 
We note Cf his(her,its) representative curve.
 
We try to determine all the points of intersection of the curve Cf and the line (AB) of coordinates whole.
 
1.Explain why this problem is to determine all integer(whole) values ​​of k such as vectors AB and AM are collinear, where M is the point of coordinates (k ; k^ 4 +2.25 k^3-44.5k^2-260k+100).