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

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

If $$a,\,b,\,c$$ are distinct $$ + ve$$ real numbers and $${a^2} + {b^2} + {c^2} = 1$$ then $$ab + bc + ca$$ is