If one root of the equation $${x^2} + px + 12 = 0$$ is 4, while the equation $${x^2} + px + q = 0$$ has equal roots,
then the value of $$'q'$$ is

If the sum of the roots of the quadratic equation $$a{x^2} + bx + c = 0$$ is equal to the sum of the squares of their reciprocals, then $${a \over c},\,{b \over a}$$ and $${c \over b}$$ are in

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