Question

Let two numbers have arithmetic mean 9 and geometric mean 4. Then find the equation which has these two numbers as its roots.

Answer 1

Let the two numbers be a and b. 

Then \(\frac{a+b}{2}\) = 9 ⇒ a + b = 18

\(\sqrt{ab}\) = 4 ⇒ ab = 16

∴ Required eqn is x² – Sum of roots x + Product of roots = 0 

⇒ x² – 18x + 16 = 0.