Let `f(x)=Ax^2+Bx+C` where A, B, C are three real constants, if f(x) is integer for integral values of x, then prove that each of 2A, (A+B) and C is an integer. Conversely, if each of 2A, (A+B) , C is an integer then f(x) will be integer for integral values of x.

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)=a+b|x|+c|x|^(2) , where a,b,c are real constants. The, f'(0) exists if

Let f(x)=a+b|x|+c|x|^(2) , where a,b,c are real constants. The, f'(0) exists if

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.

Let f(x)=A x^2+B x+c ,w h e r eA ,B ,C are real numbers. Prove that if f(x) is an integer whenever x is an integer, then the numbers 2A ,A+B ,a n dC are all integer. Conversely, prove that if the number 2A ,A+B ,a n dC are all integers, then f(x) is an integer whenever x is integer.

Let f(x)=A x^2+B x+c ,w h e r eA ,B ,C are real numbers. Prove that if f(x) is an integer whenever x is an integer, then the numbers 2A ,A+B ,a n dC are all integer. Conversely, prove that if the number 2A ,A+B ,a n dC are all integers, then f(x) is an integer whenever x is integer.

Let f(x)=A x^2+B x+c ,w h e r eA ,B ,C are real numbers. Prove that if f(x) is an integer whenever x is an integer, then the numbers 2A ,A+B ,a n dC are all integer. Conversely, prove that if the number 2A ,A+B ,a n dC are all integers, then f(x) is an integer whenever x is integer.

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.