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