Let α & β be the roots of the quadratic equation
It is given that
A.M.=α+β2=8 and √αβ=5
Thus, α+β=16 ...(1)
αβ=25 ...(2)
Now, quadratic equation is
x2 -Sum of roots)x + [Product of roots] = 0
x2−(α+β)x+(αβ)=0
Substituing α+β=16, αβ=25
from (1) & (2)
x2−16x+25=0
Thus, the required quadratic equation is
x2−16x+25=0