If x is Real, The Maximum Value Of  is:

Let α,β be the roots of the equation x² – px + r = 0 and  2β be the roots of the equation x² – qx + r = 0. Then the value of r is

The number of real roots of the equation (x + 3)⁴ + (x + 5)⁴ = 16 is

All the values of m for which both the roots of the equation x² – 2mx + m²– 1 = 0 are greater than – 2 but less than 4, lie in the interval

The expression ax² + bx + c has the same sign as of a if

If the graph of the function y = 16x² + 8(a + 5) x – 7a – 5 is strictly above the x – axis, then ‘a’ must satisfy the inequality

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

If x² – 4x + log_1/2 a does not have two distinct roots, then the maximum value of a

If the roots of the equation bx² + cx + a = 0 be expression, then for all real values of x, the expression 3b² x² + 6bcx + 2c² is

If , for all x Ïµ R, then

If the roots the equation ax² + bx + c = are real and of opposite sign then the roots of the equation α (x – β)² + β (x – α)² = 0 are