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Permutations And Combinations
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 = G^{2}
∴ Product of the roots = G^{2} = P (say)
Required quadratic equation having a and b as its roots is
or
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