Let two numbers have an arithmetic mean 9 and geometric mean 4 , then these numbers are the roots of the quadratic equation

Step-by-step solution

Let the two numbers be α , β ∴ α + β 2 = 9 and α β = 4 ⇒ α + β = 18, α β = 16 ∴ Required equation is x 2 - α + β x + α β = 0 ⇒ x 2 - 18 x + 1 6 = 0