If a, b, c Ïµ R and a + b + c = 0, Then The Quadratic Equation 3 ax2 + 3ax2 + 2bx + c = 0 Has

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

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

The real values of a for which the quadratic equation 3x² + 2 (a² + 1) x+(a² – 3a + 2) = 0 possesses roots opposite signs lie in

Let f (x) = ax2 + bx + c, a, c, Ïµ R and a ≠ 0. Suppose f (x) > 0 for all x Ïµ R.

Let g (x) = f (x) + f ’ (x) + f ”(x). Then