Question

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

Answer 1

Let the root of the quadratic equation be a and b.

So, according to the given condition,

A.M = (a + b)/2 = A
a + b = 2A ….. (1)

GM = √ab = G

ab = G²… (2)

The quadratic equation is given by,

x² – x (Sum of roots) + (Product of roots) = 0

x² – x (2A) + (G²) = 0

x² – 2Ax + G² = 0 [Using (1) and (2)]

∴ The required quadratic equation is x² – 2Ax + G² = 0.