Find a quadratic equation with integral coefficients whose roots are $\frac{α}{β}$ and $\frac{β}{α}$ The roots of the equation $2x^2-3x+6=0$ are α and β. Find a quadratic equation with integral coefficients whose roots are $\frac{α}{β}$ and $\frac{β}{α}$.
The answer is $4x^2+5x+4=0$
I don't know how to get to the answer. Could someone explain the steps? 

$$
\left( x - \frac \alpha \beta \right)\left( x - \frac\beta\alpha\right) = 0
$$
$$
(\beta x-\alpha)(\alpha x-\beta) = 0
$$
$$
\alpha\beta x^2 - (\alpha^2+\beta^2) x + \alpha \beta = 0 \tag 1
$$
If $2x^2-3x+6=0$ then $x = \dfrac{3 \pm \sqrt{-39}} 4.$ So
$$
\alpha\beta = \frac{3+\sqrt{-39}} 4 \cdot \frac{3-\sqrt{-39}} 4 = 3.
$$
$$
\alpha^2+\beta^2 = \left( \frac{3+\sqrt{-39}} 4 \right)^2 + \left( \frac{3-\sqrt{-39}} 4 \right)^2 = \frac{-30}{16} + \frac{-30}{16} = \frac{-15} 4.
$$
So line $(1)$ becomes
$$
3x^2 + \frac{15} 4 x + 3 = 0
$$
which is equivalent to
$$
4x^2 + 5x + 4 =0.
$$
