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 the roots of the equation x² – 2ax + a² + a – 3 = 0 are real and less than 3, then

If b > a, then the equation (x – a) (x – b) – 1 = 0, has

If α and β (α < β), are the roots of the equation x² + bx + c = 0, where c < 0 < b, then

If 1 lies between the roots of the equation 3x² – 3 sin α x – 2 cos² α = 0 then α lies in the interval

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