If arithmetic mean and geometric mean of roots of a quadratic equation are 8 and 5 respectively, then the quadratic equation is:

$x^2-16x+25=0$

In a quadratic equation,

arithmetic mean of roots = 8 

(a+b)/2 = 8

a+b = 16

geometric mean of roots = 5

√(ab) = 5

ab = 25

Quadratic Equation:

$x^2-(Sum of Roots)x+(Product of Roots)=0$

The correct answer is Option (3) → $x^2-16x+25=0$