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

Question

Philoid · Accepted Answer

Let the roots of the required quadratic equation be a and b.

The arithmetic and geometric means of roots are A and G respectively.

⇒ A = (a + b)/2…(i)

And G = …(ii)

We know that the equation whose roots are given is =

From (i) and (ii) we get:

Thus, is the required quadratic equation.

Ans: is the required quadratic equation.