If $$\alpha \ne \beta $$ but $${\alpha ^2} = 5\alpha - 3$$ and $${\beta ^2} = 5\beta - 3$$ then the equation having $$\alpha /\beta $$ and $$\beta /\alpha \,\,$$ as its roots is

If $$\left| {z - 4} \right| < \left| {z - 2} \right|$$, its solution is given by :

z and w are two nonzero complex numbers such that $$\,\left| z \right| = \left| w \right|$$ and Arg z + Arg w =$$\pi $$ then z equals

If $$p$$ and $$q$$ are the roots of the equation $${x^2} + px + q = 0,$$ then