Let \( \Large \alpha \), \( \Large \beta \) are the root of the required equation, then \( \Large A = \frac{ \alpha + \beta }{2} => \alpha \beta = 2A \) and \( \Large G=\sqrt{ \alpha \beta } => \alpha \beta = G^{2} \) the required equation is \( \Large t^{2}-2At+G^{2}=0 \)