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

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

If the roots of x^(2)-bx+c=0 are two consecutive integers then b^(2)-4c=

If the roots of the equation x^2-bx+c=0 are two consecutive integers then 3(b^2-4c)=

Statement 1: If a,b,c are all rational and one of the roots of the equation ax^(2)+bx+c=0 is 2-sqrt(5) then the other root is 2+sqrt(5) . Statement 2: In any quadratic equation with rational coefficients,the irrational roots always occur in the conjugate pair.

The roots of the equation x^(2)+px+q=0 are consecutive integers.Find the discriminant of the quadratic equation.

Statement -1 : A root of the equation (2^(10)-3)x^(2)-2^(11)x +2^(10)+3 =0 " is " 1 and Statemen-2 : The sum of the coefficients of a quadratic equation is zero, then 1 is a root of the equation.