The roots of the equation

There a another problem that is hard to figure. The question ask that the roots of the equation $\displaystyle 9x^2+6x+1 = 4kx $ where $\displaystyle k $ is a real constant, are denoted by $\displaystyle \alpha $ and $\displaystyle \beta$.

(a) Show that the equation whose roots are $\displaystyle \frac {1}{\alpha}$ and $\displaystyle \frac {1}{\beta}$ is $\displaystyle x^2+6x+9=4kx$

(b) find the set of values of $\displaystyle k $ for which $\displaystyle \alpha $ and $\displaystyle \beta $ are real and positive. Can anyone help me with this problem?