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

The roots of the quadratic equation $${x^2} - 2\sqrt 3 x - 22 = 0$$ are

The quadratic equation $${x^2} + 15|x| + 14 = 0$$ has