Permutations and Combinations

Question

# If A and G are respectively the A.M. and G.M. between two positive numbers a and b, then proof the quardratic equation having a, b as it roots is

Since A is the A.M. between a and b

∴                    A =                                                                 ...(i)
Since G is the G.M. between a and b

∴                                  G =                                                   ...(ii)
From (i),         a + b = 2A

∴              Sum of the roots = 2A = S (Say)
From (ii), ab = G2

∴        Product of the roots = G2 = P (say)
Required quadratic equation having a and b as its roots is
or