Let a,b,c,ma,b,c,m and nn be integers such that m<nm<n and define the quadratic function f(x) = ax^2+bx+cf(x)=ax2+bx+c where xx is real. Then f(x)f(x) has a graph that contains the points (m,0)(m,0) and (n, 2016^2)(n,20162). How many values of n-mn−m are possible?
1 Answer
Sep 15, 2016
Explanation:
The graph of
Here,
This means that
Therefore,
No. of possible values of
We have used this result : If the prime factorisation of
then