i tried to denote the roots to be $a,(a+1),b$ in this problem and i set up a bunch of equations but they are too complicated to solve. What is a way to solve this problem and check it within 3-4 minutes (you all know the time limit for contest is generally very limited)?
Let k be a positive integer and let w be an integer such that two of the roots for x of the cubic equation $x^3 - 17x^2 +kx +w=0$ are consecutive positive integers. Find the value of k if absolute value of (k-w) is a maximum.
Any answer?