Question -
Answer -
Let the root of thequadratic equation be a and b.
So, according to thegiven condition,
A.M = (a+b)/2 = A
a + b = 2A ….. (1)
GM = √ab = G
ab = G2…(2)
The quadratic equationis given by,
x2 – x (Sumof roots) + (Product of roots) = 0
x2 – x (2A)+ (G2) = 0
x2 –2Ax + G2 = 0 [Using (1) and (2)]
∴ The requiredquadratic equation is x2 – 2Ax + G2 =0.