Let’s consider the roots of the quadratic equation to be a and b.

Then, we have

A.M. = \( \dfrac{a+b}{2}=8\)

a+b = 16 ............(1)

G.M. = \( \sqrt{ab}\) = 5

ab = 25 ...........(2)

We know that,

A quadratic equation can be formed as,

x^{2 }– x (Sum of roots) + (Product of roots) = 0

x^{2} – x (a + b) + (ab) = 0

x^{2} – 16x + 25 = 0 [Using (1) and (2)]

Therefore, the required quadratic equation is x^{2} – 16x + 25 = 0

Construct a quadratic in x such that A.M. of its roots is A and G.M. is G.

Find the geometric means of the following pairs of numbers:

**(i) **2 and 8

**(ii) **a^{3}b and ab^{3}

**(iii) **–8 and –2

Insert 5 geometric means between \( \dfrac{32}{9}\) and \( \dfrac{81}{2}\).