In $$\Delta$$PQR, $$\angle$$R = $${\pi \over 2}$$. If $$\tan \left( {{P \over 2}} \right)$$ and $$\tan \left( {{Q \over 2}} \right)$$ are the roots of the equation ax² + bx + c = 0, then which one of the following is correct?

If the difference between the roots of the equation $${x^2} + kx + 1 = 0$$ is strictly less than $$\sqrt 5 $$, where $$\left| k \right| \ge 2$$, then k can be any element of the interval

If the graph of a quadratic polynomial lies entirely above X-axis, then which one of the following is correct?

If cot $$\alpha$$ and cot $$\beta$$ are the roots of the equation x² + bx + c = 0 with b $$\ne$$ 0, then the value of cot ($$\alpha$$ + $$\beta$$) is