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? 

As $\alpha+\beta=\dfrac32, \alpha\beta=\dfrac62$
let $y=\dfrac\alpha\beta\iff y+1=\dfrac3{2\beta}\iff\beta=\dfrac3{2(y+1)}$
But as $\beta$ is a root of  $$2x^2-3x+6=0$$
$$2\left(\dfrac3{2(y+1)}\right)^2-3\left(\dfrac3{2(y+1)}\right)+6=0$$
As $y+1\ne0,$ multiply both sides by $\dfrac{2(y+1)^2}3$ to find $$0=3-3(y+1)+4(y+1)^2=4y^2+5y+4$$
By symmetry, we can surmise that the same equation will be reached if we start with  $y=\dfrac\beta\alpha$
