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? 

$$\alpha'=\frac{\alpha}{\beta} ,\beta'=\frac{\beta}{\alpha}$$ now find sum and product of $\bf new$ roots
$$\quad{S'=\alpha'+\beta'\\p'=\alpha'\times \beta'\\
S'=\alpha'+\beta'=\frac{\alpha}{\beta} +\frac{\beta}{\alpha}=\frac{\alpha^2+\beta^2}{\alpha\beta}=\frac{s^2-2p}{p}=\frac{(-\frac{-3}{2})^2-2.\frac{6}{2}}{\frac{6}{2}}\\p'=\alpha'\times\beta'=\frac{\alpha}{\beta} \times\frac{\beta}{\alpha}=1}$$  then put into $$\quad{x^2-s'x+p'=0\\x^2-\frac{-5}{4}x+1=0 \to \times 4 \\4x^2+5x+4=0}$$
