An algebra problem by Abhay Kumar

Algebra Level 3

If \(\alpha\) and \(\beta\) are roots of \(x^2-px+r=0\) and \(\dfrac{\alpha}{2}\) and \(2\beta\) are roots of \(x^2-qx+r=0\). If \(\dfrac{3r}{4} = \dfrac ab (2p-q)(2q-p)\), where \(a\) and \(b\) are coprime positive integers. Find \(a+b\).