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 $${t^2}{x^2} + \left| x \right| + 9 = 0$$

Difference between the corresponding roots of $${x^2} + ax + b = 0$$ and $${x^2} + bx + a = 0$$ is same and $$a \ne b,$$ then