Question

Consider the eqn x²+2x-n =0 where n€N and n€[5,100]. Total no. Of different values of 'n' so that the given eqn has integral roots is-

Answer 1

HERE x=-1+root 1+n,-1-root1+n are the roots and when square root of 1+n is a perfect square the root is an integer.in between 5 to 100 there are 8 possibilities;clearly when n=8,15,24,35,48,63,80,100 then n+1 is a perfect square sothat the roots are integers...thank u

Answer 2

100 is not count here becoz square root of n+1 is 101 it is not a perfect square replace 100 with 99 ok.....