To find: The quadratic equation.

Given: (i) AM of roots of quadratic equation is 10

(ii) GM of roots of quadratic equation is 8

Formula used: (i) Arithmetic mean between

(ii) Geometric mean between

Let the roots be p and q

Arithmetic mean of roots p and q = 10

⇒ = 10

⇒ p + q = 20 = sum of roots … (i)

Geometric mean of roots p and q = = 8

⇒ pq = 64 = product of roots … (ii)

Quadratic equation = x² – (sum of roots)x + (product of roots)

From equation (i) and (ii)

Quadratic equation = x² – (20)x + (64)

= x² –20x + 64

x² –20x + 64