If four distinct points on the curve $y= 2x^4 + 7x^3 + 3x -5$ are colinear. Arithmetic mean of the x-coordinates of the above four points is in the form a/b where a and b are coprime. Find a+b.
I first thought that points lie on the x-axis but that is not the as this curve has only 2 real roots. Apart from this I have no idea how to solve this.
Suppose the common line has the equation $y=mx+n$. Then the $x$ coordinates of those $4$ points are the solutions to the equation: $$2x^4+7x^3+(3-m)x-5-n=0=2(x-x_1)(x-x_2)(x-x_3)(x-x_4).$$
Can you take it from here?