Construct a quadratic in x such that A.M. of its roots is A and G.M. is G.

Let the root of the quadratic equation be a and b.

According to the given condition,

⇒

⇒ a + b = 2A …..(1)

⇒ GM = √ab = G

= ab = G²…(2)

The quadratic equation is given by,

x²– x (Sum of roots) + (Product of roots) = 0

x² – x (2A) + (G²) = 0

x² – 2Ax + G² = 0 [Using (1) and (2)]

Thus, the required quadratic equation is x² – 2Ax + G² = 0.