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 p is an integers, then every square integer is of the form

For some integer q , every odd integer is of the form

For some integer m , every even integer is of the form

Let f(x)=Ax^(2)+Bx+c, where A,B,C are real numbers.Prove that if f(x) is an integer whenever x is an integer,then the numbers 2A,A+B, and C are all integer. Conversely,prove that if the number 2A,A+B, and C are all integers,then f(x) is an integer whenever x is integer.

For how many real values of k is 6kx^2 + 12kx -24x + 16 a perfect square for every integer x?

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.

Let n be a four-digit integer in which all the digits are different.If x is number of odd integers and y is number of even integers, then a.x y c.x+y=4500 d.|x-y|=54

If x is a negative integer, -x is a positive integer.