The roots of the equation $$(q - r){x^2} + (r - p)x + (p - q) = 0$$ are

The sum of all real roots of the equation $${\left| {x - 3} \right|^2} + \left| {x - 3} \right| - 2 = 0$$ is

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