If `Dgt0,a=1,b,cinZ` (integer numbers) and roots are rational,prove that the roots are integers.

Statement (1): If a and b are integers and roots of x^(2)+ax+b=0 are rational then they must be integers.Statement (2): If the coefficient of x^(2) in a quadratic equation is unity then its roots must be integers

Every integer is a rational number but a rational number need not be an integer

Every integer is a rational number but a rational number need not be an integer

Square root of a rational number

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

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.

A root of unity is a complex number that is a solution to the equation,z^(n)=1 for some positive integer nNumber of roots of unity that are also the roots of the equation z^(2)+az+b=0, for some integer a and b is

Every integer is a rational number.

Are the following statements true or false? Give reasons for your answer? Every whole number is a natural number Every integer is a rational number.Every rational number is an integer.Every natural number is a whole number.Every integer is a whole number Every rational number is a whole number