Sum Of The Non – Real Roots Of   

A quadratic equation with rational coefficients can have

If the roots of ax² + bx + c = 0 are in the ratio m: n then

For real x, the expression [(x + m)² – 4mn]/[2(x – n)] can be have any value except

If the expression y² + 2xy + 2x + my – 3 can be resolved into two rational factors, then m must be

If one root of the equation x² + px + 12 = 0 is 4, while the equation x² +px + q = 0 has equal roots, the value of q is

If x² + px + 1 is a factor of ax² + bx + c, then

If 8, 2 are the roots of x² + ax + β = 0 and 3, 3 are the roots of x² + α x+ b = 0 then the roots of x² + ax + b = 0 are

The number of real roots of 

The product of real of the equation  

              is

If tan A and tan B are the roots of the quadratic equation x² – px + q = 0, then value of sin² (A + B) is