Given: A.M. and G.M. of roots of a quadratic equation are 8 and 5, respectively.

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

Here,

A.M = = 8

⇒ a+b = 16 —1

G.M = √ab = 5

⇒ (√ab)² = 5²

⇒ ab = 25 —2

The quadratic equation is given by,

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

x² – x (a + b) + (ab) = 0

x² – 16x + 25 = 0 (From eq –1 and eq –2)

∴ The required quadratic equation is x² – 16x + 25 = 0