Trivial Q (1 Viewer)

[OLDMAN]

If 4 distinct points of the curve y=4x^4+14x^3+6x-10 are collinear, then their mean x-coordinates is a constant k. Find k.

Trivial if you find the key!

 

[ND]

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.

 

[OLDMAN]

The sum is a constant but not the points.

Anyway, nice work.