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

Given: A.M. and G.M. of roots of a quadratic equation are 8 and 5, respectively.

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

Here,

A.M = = 8

a+b = 16 —1

G.M = √ab = 5

(√ab)2 = 52

ab = 25 —2

The quadratic equation is given by,

x2x (Sum of roots) + (Product of roots) = 0

x2 x (a + b) + (ab) = 0

x2 – 16x + 25 = 0 (From eq –1 and eq –2)

The required quadratic equation is x2 – 16x + 25 = 0

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