If the value of `ax^2+bx+c` is always an integer for integral values of `x` where a, b, c are rationals then a+b must be an integer.

If x^(2)+ax+b is an integer for every integer x then

If x^2+ax+b is an integer for every integral value of x and roots of equation x^2+ax+b=0 are rational then is (A) both roots are integers (B) one is an integer and the othe is not (C) no root is an integer (D) one root is zero and other is non zero

If ax^(2)+2bx+4c=16 has no real roots and a+c>b+4 then integral value of 'c' can be

Let f (x) =ax ^(2) +bx+c, where a,b,c are integers and a gt 1. If f (x) takes the value p, a prime for two distinct integer values of x, then the number of integer values of x for which f (x) takes the value 2p is :

If a^(b^(t))=6561 ,then find the least possible value of (a.b.c), where a,b and c are integers.

If alpha and beta are equal rational numbers, roots of ax^(2)+bx+c=0 (where a,b,c be rational numbers ) then Delta=

IF (a^b)^c =729 , then find the minimum possible value of a+b+c (where a,b and c are positive integers).