It is given that the roots of the equation $${x^2} - 4x - {\log _3}P = 0$$ are real. For this the minimum value of P is

If $$\alpha$$ and $$\beta$$ are the roots of the equation 3x² + 2x + 1 = 0, then the equation whose roots are $$\alpha$$ + $$\beta$$^$$-$$1 and $$\beta$$ + $$\alpha$$^$$-$$1 is

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