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

The quadratic equation whose roots are three times the roots of $$3a{x^2} + 3bx + c = 0$$ is

If a, b, c are real, then both the roots of the equation $$(x - b)(x - c) + (x - c)(x - a) + (x - a)(x - b) = 0$$ are always

If $$\alpha$$, $$\beta$$ be the roots of the quadratic equation x² + x + 1 = 0 then the equation whose roots are $$\alpha$$¹⁹, $$\beta$$⁷ is