Let `f(x) = ax^2 + bx +c`, where `a, b, c` are rational, and `f: z->z` ,Where `z` is the set of integers. Then `a+b` is

Q cup Z = Q , where Q is the set of rational numbers and Z is the set of integers.

Q uu Z = Q , where Q is the set of rational numbers and Z is the set of integers.

Q uu Z = Q , where Q is the set of rational numbers and Z is the set of integers.

Let a,b,c be rational numbers and f:Z->Z be a function given by f(x)=a x^2+b x+c. Then, a+b is

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 :

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 :

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 number 2A, A+B and C are all integers. Conversely, prove that if the numbers 2A, A+B and C are all integer then f(x) is an integer whenever x is an integer.

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.