If both the roots of the quadratic equation x² $$-$$ mx + 4 = 0 are real and distinct and they lie in the interval [1, 5], then m lies in the interval :

The number of all possible positive integral values of $$\alpha $$  for which the roots of the quadratic equation, 6x² $$-$$ 11x + $$\alpha $$ = 0 are rational numbers is :

Let p, q and r be real numbers (p $$ \ne $$ q, r $$ \ne $$ 0), such that the roots of the equation $${1 \over {x + p}} + {1 \over {x + q}} = {1 \over r}$$ are equal in magnitude but opposite in sign, then the sum of squares of these roots is equal to :

If an angle A of a $$\Delta $$ABC satiesfies 5 cosA + 3 = 0, then the roots of the quadratic equation, 9x² + 27x + 20 = 0 are :