Q. 324.3( 54 Votes )

If A.M. and

Answer :

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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