If the roots of $2x^2+kx+3=0$, are $\alpha$ and $\beta$, what is $k$?

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The roots of the quadratic equation \(2x^2+kx+3=0\), where \(k>0\), are \(\alpha\) and \(\beta\), whilst those of the equation \(3x^2-2x+3\) are \(\frac{\alpha}{\beta}\) and \(\frac{\beta}{\alpha}\). Calculate the value of \(k\).

Since we know the roots of both equations, we could try to rewrite the quadratics in a factorised form and compare coefficients!