Permutations and Combinations

Permutations and Combinations


If A.M. and G.M. of roots of a quadratic equation are 8 and 5 respectively, then obtain the quadratic equation.


Let a, b be roots of required quadratic equation
Given   fraction numerator straight a plus straight b over denominator 2 end fraction space equals space 8                      and   square root of ab space equals 5
rightwards double arrow          a + b = 16        and ab = 25
                 S = sum of roots = a + b = 16.
and                 P = Product of roots = ab = 25
   ∴    Required quadratic equation isspace space space space space space straight x squared minus Sx plus straight P space equals 0    or   straight x squared minus 16 straight x plus 25 space equals space 0.

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