The Real Values Of a for Which The Sum Of The Squares Of The Roots Of The Equation x2 – (a – 2) x – a – 1 = 0 Assume The Least Value Is

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

Sum of the non – real roots of 

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

If x Ïµ R, the number of solution of  = 1 is

If l, m, n are real, l + m ≠ 0, then the roots of the equation

         (l + m)x² – 3(l – m)x – 2 (l + m) = 0 are

If p and q are distinct primes and x² – px + q = 0 has distinct positive roots, then p + q equals