Write the quadratic equation the arithmetic and geometric means of whose roots are A and G respectively.

Question

Philoid · Accepted Answer

Let two roots be a and b

∴ The arithmetic mean is given by

⇒

⇒ Geometric mean is given by √a.b

⇒

Quadratic equation can be written as

⇒

Where a and b are roots of given equation

Substituting AM and GM

⇒ x²-2Ax+G² = 0.