The Quadratic.

Algebra Level 2

Consider two quadratic equations \(kx^2-5x+3=0\) and \(27x^2-30x+8=0\) having roots \(\alpha,~\beta\) and \(\gamma,~\delta\) respectively. If \(\alpha,~\beta,~\gamma,~\delta\) form a geometric progression, find the value of \(k\).

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