# 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 $$a+b$$.

×