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1 Answer

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Best answer

Solution:

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

According to the given condition,

A. M. space equals fraction numerator a plus b over denominator 2 end fraction equals 8 rightwards double arrow a plus b space equals space 16 space space space space space space space space space space space space space.... left parenthesis 1 right parenthesisG. M. space equals space square root of a b end root space equals space 5 space rightwards double arrow a b space equals space 25 space space space space space space space space space space space space space space space space... left parenthesis 2 right parenthesis

The quadratic equation is given by,

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

x2 – x (a + b) + (ab) = 0

x2 – 16x + 25 = 0 [Using (1) and (2)]

Thus, the required quadratic equation is x2 – 16x + 25 = 0

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