Let a and b in the line y=ax+b be such that the line cuts the curve y=4x^4+14x^3+6x-10 in 4 places.
Solving simultaneously:
4x^4+14x^3+(6-a)x-10-b=0
Now k = (sum of roots of this eq)/4
= -14/4 * 1/4
= -14/16
Hmmm is that right? Cos it seems that no matter what a and b are, the sum of the roots would be the same, which kinda defeats the purpose of saying "4 distinct points" in the question.
