The value of '$$a$$' for which one root of the quadratic equation $$$\left( {{a^2} - 5a + 3} \right){x^2} + \left( {3a - 1} \right)x + 2 = 0$$$
is twice as large as the other is

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

Product of real roots of equation $${t^2}{x^2} + \left| x \right| + 9 = 0$$

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